And if Bush went ahead and still went to war, what would Congress do?
If they felt it to be an act of a tyrant, they would impeach him.
Bills fail all the time, many times due to wording the Congress does not like, not direct opposition to the bill's intent.
Impeachment, not refusal of bills is how Congress deals with tyranny.
Not necessarily. If Bush's party controlled congress they may let it slide. Alternatively, if Bush started using his military to round up and imprison the opposition's leaders they probably wouldn't impeach him either.
Bills fail all the time, many times due to wording the Congress does not like
...and you have offered absolutely no evidence whatsoever that Congress was simply upset at the "wording" of Lincoln's bill when they killed it. Much to the contrary, the congressional record is full of stated objections to the bill's intent itself to the point that members specifically sought out assurances that other military bills did not try to slip in a habeas corpus suspension through the back door.
There's no way around it, ftD. Lincoln went to congress and used his joint address to ask congress for a habeas corpus suspension. His habeas corpus bill was then designated S. 1 as the most important piece of legislation of the session. In a clear and direct rejection of Lincoln's request, Congress killed the very same bill he explicitly and publicly pled with them to pass.