There is no right wing in US politics

[Andrew D]

That depends. If there is no money in the budget which Congress has appropriated for that purpose and no money the spending of which has been left to the President's discretion, then it would be unconstitutional for the President to use any US public money to fund an invasion of Iran. (See U.S. Const., Art. I, Sec. 9 ("No Money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law").)

If there is money in the budget which the President can constitutionally spend on an invasion of Iraq, Congress can pass a law forbidding the use of US funds for that purpose. But the President can still veto such a bill, so it would have to be re-passed by two-thirds majorities in the House of Representatives and the Senate. If the President's veto were overridden, it would be unconstitutional for the President to spend any US funds for that purpose.

If the President decides to invade Iran using US funds despite the unconstitutionality of his doing so, one hopes that the generals, etc., would refuse to carry out that invasion. Military personnel at all levels are taught that it is their duty to refuse to obey unlawful orders, and an unconstitutional invasion of another country would be about as unlawful as it gets.

Whether the generals, etc., go along with the invasion or not, Congress can remove the President from office. That requires a majority vote in the House of Representatives, a trial in the Senate (with the Chief Justice presiding) and a two-thirds vote in the Senate for conviction.

No President has ever been removed from office by impeachment and conviction. Two -- Andrew Johnson and Bill Clinton -- have been impeached by the House, but neither was convicted by the Senate. (Johnson survived conviction by one vote. Clinton survived conviction easily; the Republicans were unable to muster even a simple majority of votes for conviction, let alone the two-thirds majority required.)