Here's how it has been working lately. A spending bill comes up - Congress wants 400 billion, Bush say he'll veto anything over 375 bil, they send him a 389 billion bill, and he signs it.
For me, a big spender President would ask if 400 was enough, how about 410? An obstructionist President would veto anything over 350, force a veto override and lose support for any of his pet bills (oh say like defense spending for the war), a realist conservative would slow spending as much as possible while using the compromise to build up support for key issues....like the war.
But that means knowing you'll win some and lose some in the nasty system of Washington. ('Democracy is a terrible form of government but it is better than anything else' attitude)
A conservative leader would say that the war on terror is expensive, and therefore we have to sacrifice by cutting back on wasteful social spending. Anyone who gets upset and therefore wants to oppose the war on terror can suffer in the next election.
At least a conservative leader wouldn't initiate pet bills that dramatically expand government.