"Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States: If he approve he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated, who shall enter the Objections at large on their Journal, and proceed to reconsider it," continues the Constitution, "If after such Reconsideration two thirds of that House shall agree to pass the Bill, it shall be sent, together with the Objections, to the other House, by which it shall likewise be reconsidered, and if approved by two thirds of that House, it shall become a Law.
"The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts ... To borrow Money on the credit of the United States," notes the Constitution.
The power in this battle resides in Congress, specifically in the House of Representatives, as the originator of all appropriation bills. The people elect the House of Representatives every two years -- therefore the power resides with the people. While the president and the Senate majority leader might hold the power of the media and messaging, as well as the bully pulpit -- the House has the constitutional power to start appropriations.
Is it frustrating to watch our government fail to work efficiently and effectively? Well, yes, but it is much better than the alternative. Efficiency and rapid action can be achieved by having a single point of control, a king or dictator who makes a decision and forces those around him (or her) to carry out the decision. However, it is exactly this structure -- a king -- which our founding fathers guarded against. They knew that the power must be divided, and they deliberately created a government with three branches that included checks and balances within the system itself.
Dysfunctional -- yes, on occasion -- but better than the alternative.