That is correct. From the US Department of Justice:
[quote]First, it is clear that the Constitution secures all federal executive power in the President to ensure a unity in purpose and energy in action. “Decision, activity, secrecy, and dispatch will generally characterize the proceedings of one man in a much more eminent degree than the proceedings of any greater number.” The Federalist No. 70, at 392 (Alexander Hamilton). The centralization of authority in the President alone is particularly crucial in matters of national defense, war, and foreign policy, where a unitary executive can evaluate threats, consider policy choices, and mobilize national resources with a speed and energy that is far superior to any other branch. As Hamilton noted, “Energy in the executive is a leading character in the definition of good government. It is essential to the protection of the community against foreign attacks.” Id. at 391. This is no less true in war. “Of all the cares or concerns of government, the direction of war most peculiarly demands those qualities which distinguish the exercise of power by a single hand.” Id. No. 74, at 415 (Alexander Hamilton). (9)
Second, the Constitution makes clear that the process used for conducting military hostilities is different from other government decisionmaking. In the area of domestic legislation, the Constitution creates a detailed, finely wrought procedure in which Congress plays the central role. In foreign affairs, however, the Constitution does not establish a mandatory, detailed, Congress-driven procedure for taking action. [b]Rather, the Constitution vests the two branches with different powers - the President as Commander in Chief, Congress with control over funding and declaring war [/b]- without requiring that they follow a specific process in making war. By establishing this framework, the Framers expected that the process for warmaking would be far more flexible, and capable of quicker, more decisive action, than the legislative process. [b]Thus, the President may use his Commander-in-Chief and executive powers to use military force to protect the Nation, subject to congressional appropriations and control over domestic legislation.[/b]
Third, the constitutional structure requires that any ambiguities in the allocation of a power that is executive in nature - such as the power to conduct military hostilities - must be resolved in favor of the executive branch. Article II, section 1 provides that "[t]he executive Power shall be vested in a President of the United States." U.S. Const. art. II, § 1. By contrast, Article I's Vesting Clause gives Congress only the powers "herein granted." Id. art. I, § 1. This difference in language indicates that Congress's legislative powers are limited to the list enumerated in Article I, section 8, while the President's powers include inherent executive powers that are unenumerated in the Constitution. To be sure, Article II lists specifically enumerated powers in addition to the Vesting Clause, and some have argued that this limits the "executive Power" granted in the Vesting Clause to the powers on that list. But the purpose of the enumeration of executive powers in Article II was not to define and cabin the grant in the Vesting Clause. Rather, the Framers unbundled some plenary powers that had traditionally been regarded as "executive," assigning elements of those powers to Congress in Article I, while expressly reserving other elements as enumerated executive powers in Article II. So, for example, the King's traditional power to declare war was given to Congress under Article I, while the Commander-in-Chief authority was expressly reserved to the President in Article II. Further, the Framers altered other plenary powers of the King, such as treaties and appointments, assigning the Senate a share in them in Article II itself. (10) Thus, the enumeration in Article II marks the points at which several traditional executive powers were diluted or reallocated. Any other, unenumerated executive powers, however, were conveyed to the President by the Vesting Clause.
[b]There can be little doubt that the decision to deploy military force is "executive" in nature, and was traditionally so regarded[/b]. It calls for action and energy in execution, rather than the deliberate formulation of rules to govern the conduct of private individuals. Moreover, the Framers understood it to be an attribute of the executive. "The direction of war implies the direction of the common strength," wrote Alexander Hamilton, "and the power of directing and employing the common strength forms a usual and essential part in the definition of the executive authority." The Federalist No. 74, at 415 (Alexander Hamilton). As a result, to the extent that the constitutional text does not explicitly allocate the power to initiate military hostilities to a particular branch, the Vesting Clause provides that it remain among the President's unenumerated powers.
Fourth, depriving the President of the power to decide when to use military force would disrupt the basic constitutional framework of foreign relations. From the very beginnings of the Republic, the vesting of the executive, Commander-in-Chief, and treaty powers in the executive branch has been understood to grant the President plenary control over the conduct of foreign relations. As Secretary of State Thomas Jefferson observed during the first Washington Administration: "the constitution has divided the powers of government into three branches [and] has declared that the executive powers shall be vested in the president, submitting only special articles of it to a negative by the senate." Due to this structure, Jefferson continued, "the transaction of business with foreign nations is executive altogether; it belongs, then, to the head of that department, except as to such portions of it as are specially submitted to the senate. Exceptions are to be construed strictly." Thomas Jefferson, Opinion on the Powers of the Senate (1790), reprinted in 5 The Writings of Thomas Jefferson, at 161 (Paul L. Ford ed., 1895). In defending President Washington's authority to issue the Neutrality Proclamation, Alexander Hamilton came to the same interpretation of the President's foreign affairs powers. According to Hamilton, Article II "ought . . . to be considered as intended . . . to specify and regulate the principal articles implied in the definition of Executive Power; leaving the rest to flow from the general grant of that power." Alexander Hamilton, Pacificus No. 1 (1793), reprinted in 15 The Papers of Alexander Hamilton, at 33, 39 (Harold C. Syrett et al. eds., 1969). As future Chief Justice John Marshall famously declared a few years later, "The President is the sole organ of the nation in its external relations, and its sole representative with foreign nations. . . . The [executive] department . . . is entrusted with the whole foreign intercourse of the nation . . . ." 10 Annals of Cong. 613-14 (1800). Given the agreement of Jefferson, Hamilton, and Marshall, it has not been difficult for the executive branch consistently to assert the President's plenary authority in foreign affairs ever since.
[b]In the relatively few occasions where it has addressed foreign affairs, the Supreme Court has agreed with the executive branch's consistent interpretation. Conducting foreign affairs and protecting the national security are, as the Supreme Court has observed, "'central' Presidential domains." [/b]Harlow v. Fitzgerald, 457 U.S. 800, 812 n.19 (1982). The President's constitutional primacy flows from both his unique position in the constitutional structure, and from the specific grants of authority in Article II that make the President both the Chief Executive of the Nation and the Commander in Chief. See Nixon v. Fitzgerald, 457 U.S. 731, 749-50 (1982). Due to the President's constitutionally superior position, the Supreme Court has consistently "recognized 'the generally accepted view that foreign policy [is] the province and responsibility of the Executive.'" Department of the Navy v. Egan, 484 U.S. 518, 529 (1988) (quoting Haig v. Agee, 453 U.S. at 293-94). "The Founders in their wisdom made [the President] not only the Commander-in-Chief but also the guiding organ in the conduct of our foreign affairs," possessing "vast powers in relation to the outside world." Ludecke v. Watkins, 335 U.S. 160, 173 (1948). This foreign affairs power is exclusive: it is "the very delicate, plenary and exclusive power of the President as sole organ of the federal government in the field of international relations - a power which does not require as a basis for its exercise an act of Congress." United States v. Curtiss-Wright Export Corp., 299 U.S. 304, 320 (1936).
[b]Conducting military hostilities is a central tool for the exercise of the President's plenary control over the conduct of foreign policy.[/b] There can be no doubt that the use of force protects the Nation's security and helps it achieve its foreign policy goals. Construing the Constitution to grant such power to another branch could prevent the President from exercising his core constitutional responsibilities in foreign affairs. Even in the cases in which the Supreme Court has limited executive authority, it has also emphasized that we should not construe legislative prerogatives to prevent the executive branch "from accomplishing its constitutionally assigned functions." Nixon v. Administrator of General Servs., 433 U.S. 425, 443 (1977).[/quote]
usdoj.gov/olc/warpowers925.htm
Note also the very topic of the web page talks about the War Powers Resolution and the Joint Resolution passed three days after 9/11 which specifically granted the President broad Executive power to
[quote][b]retaliate against any person, organization, or State suspected of involvement in terrorist attacks on the United States, but also against foreign States suspected of harboring or supporting such organizations.
The President may deploy military force preemptively against terrorist organizations or the States that harbor or support them, whether or not they can be linked to the specific terrorist incidents of September 11.[/b] [/quote]
Does that clarify things a bit?