Updates:

3:06: Boehner and Reid left their meeting at the White House without a deal in hand Thursday afternoon. They'll head back for a fourth meeting with Obama at 7 p.m. "All of us believe we can get to an agreement, but we're not there yet," Boehner said.

2:54: The House has passed a weeklong budget stopgap, despite Senate Democrats' promise not to vote on it and Obama's threaten to veto it. A few Republicans voted against the measure, and more than a dozen Democrats voted for it, The Hill's Pete Kasperowicz reports.

2:35: Politico reports that Boehner wants $39 billion in spending cuts, and that Democrats countered with $34 billion to $35 billion in cuts. But policy riders remain a sticking point.

2:20: The Office of Management and Budget has begun telling federal employees if they'll be furloughed during a shutdown as the White House "ramps up its contingency plans," The Hill's Sam Youngman reports.

1:17: Republicans are now calling their budget stopgap a "troop funding bill" because it would keep federal doors open an extra week but find the military for the rest of the year. The short-term funding would make sure soldiers get their paychecks as Congress continues to negotiate. But Slate's Dave Weigel notes that the Democrats' proposal, which cut just $6 billion in spending, also would have funded troop paychecks for the rest of the year, and that "went down in flames." Nevertheless, Boehner hammered Obama for threatening to veto a stopgap and thus not funding the troops.

12:25: Obama says he'd veto the House GOP's one-week stopgap budget, The Hill 's Sam Youngman reports. But the president would be open to a "clean" continuing resolution.

12:10: The major roadblocks to a budget deal are policy riders that would change abortion and environmental regulations, the Associated Press' Andrew Taylor reports. Republicans want to use the bill to ban taxpayer-funded abortions in Washington, D.C., cancel funding to non-profits that provide abortions overseas, and end funding of Planned Parenthood. Another rider would prevent the EPA from regulating greenhouse gases.

The Weekly Standard's John McCormack notes that Reid is essentially saying the Senate would be willing, despite earlier indications to the contrary, to vote for another stopgap bill that would fund the government an extra week past the April 8 deadline.

11:35: Boehner and Reid will go back to the White House for their third budget meeting with Obama, Politico's Jake Sherman and John Bresnahan report. The parties are struggling to come to an agreement over policy riders attached to the bill concerning abortion and pollution. Republicans met at 11 a.m. Thursday, but Boehner wouldn't say what was said. House Republicans are still pushing yet another stopgap--this one would fund the government for a week and the military for six months--even though Senate Democrats say there's no way they're passing such a thing. Politico reports that since the Senate hasn't offered much to "break the logjam," Republicans are daring them to ignore it.

11:10: Some lawmakers are promising not to take a paycheck if the government shuts down. But Slate's Dave Weigel calls this a "massive dodge" as congressional salaries aren't big enough to make any real dent in spending.

11:00: Reid says he expects a government shutdown, National Journal's Dan Friedman reports. Reid told a group of constituents Thursday morning that, "The numbers are basically there... But I am not near as optimistic--and that’s an understatement--as I was 11 hours ago."

House Republicans began debating a stopgap bill that would keep the government from closing down for an extra week--but keep the military funded for the rest of the fiscal year--though Senate Democrats have rejected such a plan.

What we know now: There were teeny signs of progress in the budget negotiations last night as House Speaker John Boehner and senate Majority Leader Harry Reid headed into yet another meeting with President Obama. All three left the meeting feeling optimistic, but no deal was reached. Both Republicans and Democrats face huge pressure to avoid a shutdown, which was disastrous for then-House Speaker Newt Gingrich in 1995. But Boehner faces considerable pressure from the Tea Party to demand all of the $61 billion in spending cuts that the House passed earlier this year.