The federal government lurched into a shutdown after midnight on Tuesday, after Democrats in Congress refused to back a Republican-written plan to keep funding flowing.

Unlike many past shutdown stalemates, the current fight is not over any policy provision or funding item that the G.O.P. included in its spending plan. Instead, it is a demand by Democrats for add-ons: more than $1 trillion for health care programs, and limits on President Trump’s spending power.

Democrats are demanding that Republicans, who hold a governing trifecta, negotiate on those terms before they agree to lend their votes to a bill needed to reopen the government.

Given that Congress failed to enact spending bills for the fiscal year that began on Wednesday, an extension is needed to fund the government. Both parties proposed legislation to do so temporarily to buy more time for a deal, but both bills have repeatedly failed to gain the bipartisan backing necessary to move forward in the Senate.

Here is what to know about the dueling proposals.

Republicans want a simple funding patch.

The Republican bill would fund the government largely at current spending levels through Nov. 21. It is known as a clean continuing resolution, or C.R., meaning that it would continue existing funding without any policy add-ons.

The House passed the measure last month, with all but one Democrat opposed. But in the Senate, it needs 60 votes to advance. It has fallen short of that threshold three times, most recently on Wednesday.

Democrats have denounced the measure as “partisan,” because Republicans did not negotiate with them. But unlike many partisan stopgap measures of the past, it does not contain any conservative policy dictates or spending cuts that are considered poison pills by Democrats.

Still, Democrats argue that asking them to supply the votes for a funding extension that does not address their priorities is unreasonable. They are determined to use their leverage in the spending fight to exact concessions from Mr. Trump and Republicans.

Democrats want health care money and guardrails on Trump.

The Democratic measure is also a continuing resolution, which would fund the government through Oct. 31. But it is far from clean. It would tack on more than $1 trillion for health care programs and tie Mr. Trump’s hands with congressionally approved funding.

The bill would permanently extend Obamacare subsidies that are set to expire at the end of the year, and reverse deep cuts to Medicaid enacted over the summer as part of the president’s tax cut law.

Democrats argue that Congress must act urgently to do both. If the Obamacare tax credits lapse, an estimated four million people could lose coverage starting in 2026, and prices would spike for more than 20 million people.

Some Republicans have indicated that they might support extending the Obamacare subsidies at some level. But Senator John Thune of South Dakota, the majority leader, has insisted he would not do so as part of a stopgap spending bill. He has called Democrats’ attempt to tie the two together a hostage-taking exercise.

Republicans have balked altogether at rolling back the Medicaid cuts, which helped to pay for the large tax cuts they enacted in July. In doing so, the G.O.P. has used a misleading talking point to accuse Democrats of demanding free health care for unauthorized immigrants in exchange for funding the government.

The Democrats’ temporary spending bill contains no such proposal. But because it repeals the Medicaid provisions in Republicans’ tax law, it would undo a provision that reduced, but did not eliminate, the funding that hospitals receive for emergency services provided to certain immigrants, both documented and undocumentd, in states that have expanded Medicaid under the Affordable Care Act.

Democrats also included language in their stopgap measure that would limit Mr. Trump’s ability to freeze federal funds already approved by Congress and restore money for public radio and television stations that the White House clawed back over the summer.

Both parties want security funding — but disagree on how much.

The two bills both contain spending increases for security for government officials, including members of Congress. But Democrats want to provide far more than Republicans.

Lawmakers have been increasingly concerned about threats after the recent assassinations of the right-wing activist Charlie Kirk and Melissa Hortman, a Democratic state lawmaker in Minnesota, who was killed along with her husband in June.

Republicans included $88 million to fortify security for executive branch officials, Supreme Court justices, other federal judges and congressional lawmakers in response to a rise in threats.

Democrats are asking for more. Their bill contains more than $186 million for lawmaker security on Capitol Hill and in local districts, and $140 million for Supreme Court justices and other federal judges. They did not request additional security funds for the executive branch.