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WASHINGTON -- President Obama signed a stopgap funding bill Wednesday to keep the federal government open into March, a temporary truce until Republicans and Obama rejoin the battle over the budget next year.

The bill was passed by the House Tuesday evening just hours after speeding through the Senate. President Obama signed it Wednesday within a "24-hour grace period," a White House official told Fox News.

The measure would freeze agency budgets at current levels. That's still too high for Republicans set to take over the House, who vow to cut many programs to levels in place when Obama took office. That will be difficult to achieve, even though Republicans will control the House and possess greater strength in the senate.

The bill would also create hardship at the Pentagon and the Homeland Security Department, which will be denied funding increases until their budgets pass next year.

The measure is needed because the Democratic-controlled Congress -- in an unprecedented failure to complete its most basic job on passing a budget -- has failed to enact a single one of the 12 annual spending bills that fund the day-to-day operations of every federal agency.

The House cleared the bill for Obama on a 193-165 vote after a 79-16 vote in the Senate.

Republicans promise to try next year to cut most domestic agency budgets back to pre-Obama levels. Such cuts would exceed 20 percent for some agencies.

Republicans say such cuts would produce savings of $100 billion compared to Obama's February budget request. But with the government operating at current levels for almost half of the fiscal year, the actual savings that Republicans might be able to accomplish are likely to be considerably smaller. The budget year began Oct. 1.

Republicans will have increased leverage, but Democrats will retain control of the Senate and the White House. The threat of a government shutdown is real if Democrats and resurgent Republicans can't agree.

In fact, additional stopgap spending measures may be needed next year if the battle drags on, as seems likely.

At issue is the approximately one-third of the budget passed each year by Congress to fund the 15 Cabinet departments and other agencies. The rest of the budget is dominated by benefit programs like Social Security, Medicare, and the Medicaid health care program for the poor and disabled.

Republicans haven't been very specific about which programs they want to cut next year, though they promise to rescind unspent money from last year's economic stimulus law, including billions of dollars for high-speed rail projects that critics say are likely to turn out to be boondoggles.

"Right now, there's a lot of posturing, a lot of slogans. I think they're going to go for a lot of quick, symbolic victories -- no earmarks, trying to recapture unspent stimulus," Sen. Barbara Mikulski, a liberal Democrat from Maryland, said of pet spending projects and the economic stimulus measure. "Then I think they'll start with women and children. And I will be combat ready."

The cuts are likely to come almost exclusively from domestic programs that have gotten boosts on the order of 10 percent a year since Obama took office.

Democrats warn that cutting spending is easier said than done.

"I think Republicans will discover that it's a lot easier to talk about cutting $100 billion than actually identifying the specific lines in the budget that they want to cut," said Sen. Tom Harkin, D-Iowa. "Do they really want to cut 21 percent from child care subsidies for working families -- in this economy? Do they really want to cut 21 percent from job training programs -- in this economy?"

An option under discussion among Republicans is to keep the domestic agencies running mostly on autopilot through next October but at lower spending rates.

At the same time, Republicans have promised to actually increase spending for the Pentagon and the Veterans Affairs and Homeland Security departments.

Senate Republicans last week blocked a move by Democrats to advance an almost $1.3 trillion spending bill to wrap up the unfinished budget work. The 1,924-page measure contained more than 6,700 home-state pet projects that Republicans have promised to give up.

The measure makes only a handful of funding adjustments from current levels, for example by cutting the Census budget way back since the decennial count has been completed.

It also implements Obama's recent proposal to freeze the salaries of federal civilian workers for two years.

The measure also provides $5.7 billion for the Pell Grant program, which provides grants of up to $5,550 to college students from low income families.

The Associated Press contributed to this report.