The functional mechanism behind the ongoing, completely unnecessary federal government shutdown is the failure of the two chambers of Congress to agree upon a "continuing resolution" providing the required funds for continued operations of the United States governent.
A continuing resolution is a measure to continue funding the federal government at pre-approved levels without debating a new spending bill. It is not an increase in spending, but rather an agreement to continue funding programs and expenditures at previous rates until a new budget can be negotiated between Republicans and Democrats.
Democrats want a "clean" continuing resolution, or one that allows the government to continue running with no strings attached. These funding levels were approved by both houses of Congress, including the GOP-dominated House of Representatives which is now threatening to shut down the government unless Obamacare implementation is delayed by one year and a tax on medical devices is repealed.
Normally, such resolutions are uncontroversial. But this time around, the far-right wing of the Republican Party appears to be in the driver's seat, and that's why the GOP is refusing to pass a resolution that does not include provisions attacking the Affordable Care Act. This is of course anathema to Democrats, thus ensuring the shutdown continues until one side or the other caves or a compromise is reached.
And on October 17, the U.S. debt ceiling will again be hit, meaning we're going to see another round of standoffs and pointed fingers — except a failure to reach agreement on that issue won't just mean a government shutdown, but a default on U.S. governmental debt and all the catastrophe that could ensue.