Budget policy is normally made by Congress passing budget bills which the President signs. These bills last a certain amount of time, usually ending by the beginning of the fiscal year, October 1. If the normal budget bills are not ready by then, Congress traditionally passes a 'continuing resolution' that keeps the government open with spending at the same rate as the previous year. These continuing resolutions usually last a few weeks or months giving Congress time to pass the normal budget bills. There have been continuing resolutions every year since the late 1990s.
This year the Republicans tried to kill Obamacare by refusing to pass a 'clean' continuing resolution (a 'clean' resolution has no other stuff attached, it just funds the government). At first they insisted on a continuing resolution that also eliminated all funding for Obamacare. When that didn't work, they insisted on a partial elimination. Meanwhile there's been a partial government shutdown since there is no funding bill for this fiscal year. This has caused lots of problems, so the Republicans are now trying to pass partial continuing resolutions for parts of the government they like.
Obviously, this is an incredibly stupid way to govern a country. If the Democrats give in and allow Republicans to stunt Obamacare this time, the whole process will repeat itself in a few weeks or months when another continuing resolution will be needed, or when the debt ceiling needs to rise to avoid the government welching on its debt. The Republicans will want more, of course. They'll sense the blood in the water.
There are only two possible good results from this mess:
- The Republicans are crushed, good governance wins, and a clean continuing resolution is passed. It would help if the Republicans then lost big in the 2014 election. That will put an end to government shutdowns for awhile
- Some concessions are made in exchange for taking this whole strategy off the table. For example: eliminate the concept of a debt ceiling and make continuing resolutions automatic. This would eliminate government shutdowns indefinitely. You can still cut government spending, just use the normal legislative process.
The short story: if you want good governance, don't put blood in the water. It makes the sharks attack.