A declaration of war is like any other law passed by Congress; both houses must pass it, and the president can veto it (and the veto can theoretically be overridden by a 2/3 vote in both houses).
It turns out that this is more complicated than I thought!
"Surprisingly, given the wealth of literature on the original intent of the War Powers Clause, no scholar has argued that the original understanding was that the President could not veto a declaration of war. This is particularly striking because modern scholars have argued on textualist grounds that the War Powers Clause means precisely what it says--that 'Congress shall have power . . . To declare War'--and the President cannot veto such declarations. [FN189] Only two scholars, Dean Ely and Gregory Sidak, have even raised the possibility that the original understanding was that the President could not veto declarations of war, and they dismiss the possibility rapidly. [FN190] Instead, they argue on purely textual ground that declarations of war fall within Article I, Section 7, Clause 3 of the Constitution, the Presentment Clause, which requires that every congressional 'Order, Resolution, or Vote' be presented to the President for his signature or veto. [FN191] The problem
with this argument is that the Framers understood the Presentment Clause narrowly. That is, if all congressional orders, resolutions, and votes must be presented to the President, this presumably applies, not just to declarations of war, but also to congressional proposals for constitutional amendments. However, in the 1798 case Hollingsworth v. Virginia, [FN192] the one early Presentment Clause case, the Supreme Court rejected the claim that the Eleventh *728 Amendment was invalid because it had not been signed by the President. The Court observed that the Presentment Clause 'applies only to the ordinary cases of legislation . . . .' [FN193] A congressional declaration of war, like a congressional decision to propose amendments, would seem to fall outside the category of 'ordinary cases of legislation.'
"The other principal piece of evidence on which Ely and Sidak rely is that Madison signed the declaration of war against England which Congress passed in 1812. [FN194] But Presidents sign documents for political reasons--even when they know the signature has no legal consequence--in order to highlight a personal endorsement. For example, despite Hollingsworth, on the eve of the Civil War, President Buchanan signed the congressionally-approved Corwin Amendment, which would have barred subsequent amendments banning slavery, [FN195] and President Lincoln signed the Thirteenth Amendment after it was approved by Congress in 1865. [FN196] The real question is not whether Madison signed the declaration, but what significance he attached to that signing. Evidence of Madison's intent can be found in his previously-quoted message to Congress and his proclamation following the declaration of war. Neither document is discussed by Ely or Sidak. Both documents, however, clearly state that the decision whether to go to war is purely congressional. According to Madison's war message, '[T]he Constitution wisely confides [the decision about whether to go to war] to the legislative department of the Government.' [FN197] And, according to Madison's proclamation, '[The Members of] Congress . . . have declared [war] by their act.' [FN198] The President is not part of the process. Ely's and Sidak's position is further undercut by the evidence concerning the 1798 controversy over whether to go to war with France (a subject that neither discusses). [FN199]"
https://web.archive.org/web/2007040...culty/yooj/courses/forrel/reserve/treanor.htm