* Devil lies in the details as staffers work out deal
* Democrats want to protect education, research
* Republicans skeptical of benefit savings (Adds Tea Party rally, White House comment, detail)
By Andy Sullivan
WASHINGTON, March 31 (Reuters) - Though lawmakers may have tentatively agreed to the largest domestic spending reduction in U.S. history, they now must delve into the details to decide which programs to cut to meet their $33 billion target.
One day after Republican and Democratic leaders agreed on the outlines of a budget deal that could avert a government shutdown, they jockeyed on Thursday to protect areas where they fear it will do the most harm.
“What we cut is much more important than how we cut,” Senate Democratic Leader Harry Reid said.
Staffers met shortly after Reid spoke to fill in the blanks on the agreement, which would settle a months-long battle over government spending and provide a final funding structure for the current fiscal year, which is already halfway over.
The talks could still fall apart, but neither party is eager to cause a government shutdown that could lead to thousands of layoffs when voters are nervous about the shaky economic recovery and rising gas prices brought on by unrest in the Middle East.
“There are hurdles to clear before we get from here to a deal but ... progress is being made,” White House spokesman Jay Carney told reporters.
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No matter the shape of the agreement, it would represent a big victory for Republicans, who have vowed to scale back the size of government. They will get additional opportunities in the coming months as Congress faces a vote to raise the $14.3 trillion debt ceiling and begins work on a budget for the next fiscal year, which starts on Oct. 1.
Republicans say the final size of the cut is still in flux as negotiators have to resolve whether to include funding restrictions that would prevent President Barack Obama from pursuing some of his top priorities.
“There’s no agreement on numbers” yet, House Speaker John Boehner said at a news conference.
A cut of $33 billion this fiscal year could mean severe pain for many domestic agencies. But it would do little to plug a budget deficit that is projected to hit $1.4 trillion this year.
The government has been operating on a temporary extension of last year’s budget for the past six months, but that arrangement expires on April 8.
The Democratic-led Senate and the Republican-controlled House of Representatives must pass any agreement before then. Boehner may encounter resistance from newly elected lawmakers affiliated with the grassroots Tea Party movement who have shown little appetite for compromise.
Several hundred Tea Party supporters held a rally across the street from the U.S. Capitol, demanding that Republicans stand firm on their original budget plan, which would cut $61 billion and defund Obama priorities like healthcare reform.
“Grow a spine -- no compromise,” read a hand-written sign held by Helene Kerns of West Virginia.
The Republican plan would impose immediate cuts averaging 25 percent on nearly every aspect of the government’s nonmilitary operations, from food-safety inspections to tax enforcement.
Many of the funding restrictions in that bill are unacceptable to Obama and his fellow Democrats, though some will likely make it into the final bill.
The Republican plan includes relatively minor restrictions that, for example, block assistance to mohair farmers.
Obama wants education, scientific research and other programs that lead to long-term economic growth to be spared.
On Thursday, Reid said programs that help children, retirees and working families should be protected. He mentioned the Head Start preschool program, which would face a 28 percent cut under the Republican plan. Advocates say that would cut off aid to 200,000 children.
“There’s only so much that the middle class in this country can take,” Reid said on the Senate floor.
Democrats hope to steer some cuts toward programs like crop subsidies and transportation projects that normally lie beyond the reach of the annual budget process. Republicans suspect those cuts may amount to budget gimmickry that will not lead to actual savings.
Senate Republicans are expected to unveil a measure that would amend the U.S. Constitution to require a balanced federal budget each year. It is not expected to become law but could provide leverage in upcoming budget fights. (Additional reporting by Thomas Ferraro, Richard Cowan, Caren Bohan and Alister Bull; Editing by Deborah Charles and Doina Chiacu)