Final answer:
Congress has the power to modify the annual budget, enact appropriations, control deficit spending through PAYGO and other mechanisms, and pass continuing resolutions to avoid a government shutdown. If disagreements with the President arise, Congress may need to address vetoes or work around them.
Step-by-step explanation:
Once the annual budget is set, Congress has various powers. They can scrutinize the budget through appropriations committees, making specific allocations for various spending areas like health, education, and defense. If the President disagrees with the modified budget, he can veto it, which would then require Congress to either revise it or attempt to override the veto with a two-thirds majority in both houses.
Another part of Congress's powers is the implementation of the PAYGO system, which ensures that any tax or mandatory spending increases are offset by equivalent deficit reductions. Congress also has the authority to control deficit spending through statutory deficit-control mechanisms, which can trigger sequestration to maintain fiscal balance.
If the President and Congress cannot reach an agreement on the budget, a continuing resolution may be passed to provide temporary funding, failing which a government shutdown might occur. This occurred in 1995, 1995-96, and 2013 over various policy disputes.