As federal officials began formal preparations for a government shutdown, House and Senate leaders struggled Monday to reach agreement over tens of billions of dollars in spending cuts that would avert the federal work stoppage.

After weeks of negotiating over money, time is now also a major concern. There is general agreement that the two sides must work out a deal by Tuesday night if it is to work its way through both chambers and reach President Obama’s desk before the government runs out of money Friday.

Late Monday, a senior White House aide told top agency officials to begin preparations for how to handle a shutdown, a move that was echoed in a statement by Speaker John A. Boehner (R-Ohio) to House leaders.

But Boehner also announced his intention to offer Obama and Senate Democrats another stopgap funding measure that would keep federal funding flowing for an additional week. That offer would come with conditions, however: According to the House Appropriations Committee, Democrats would have to agree to $12 billion in further spending cuts and to fund the Defense Department for the remainder of the year — thus removing the Pentagon from the possible budget disruptions still faced by other federal agencies.

Short of a broad deal for the entire federal government, approving another short-term measure may be the only route to keep Washington open while the two sides work out their differences.

Many Democrats and Republicans have said they would not approve what would be the seventh stopgap funding bill since October, but some key conservative lawmakers said Monday that they would support one week’s funding if the bill included the Pentagon’s yearly spending. Defense Secretary Robert M. Gates has been pleading with Congress to exempt his department from the piecemeal plans for funding the government a few weeks at a time.

If lawmakers cannot reach an agreement, the first federal government shutdown since the mid-1990s would start Saturday and the full impact would be felt on Monday, when millions of federal employees across the country would typically report for work.

As the deadline neared, Boehner and Senate Majority Leader Harry M. Reid (D-Nev.) exchanged insults, each side blaming the other for the stalemate.

Boehner continued to deny that he had agreed to a widely reported compromise with Democrats of $33 billion in spending reductions — even as one of his GOP chairmen worked with Democrats to hit that mark.

“Despite attempts by Democrats to lock in a number among themselves, I’ve made clear that their $33 billion is not enough, and many of the cuts that the White House and Senate Democrats are talking about are full of smoke and mirrors. That’s unacceptable,” Boehner said in a statement.

Speaking on the Senate floor, Reid insisted that “we agreed upon a number.” He accused Boehner of backing away from the compromise because of pressure from tea party activists who provided much of the energy in the GOP’s massive victory in the 2010 elections.

Many conservative Republicans in the House have said they would not vote for any budget deal unless it contained the full $61 billion in cuts GOP members approved earlier this year in a party-line vote. That measure was later rejected by the Senate, which is controlled by Democrats.

“Republicans and the tea party continue to reject reality, and insist instead on ideology,” Reid said.

At issue, according to aides familiar with the talks, is the makeup of the spending cuts. Democrats want to reach the $33 billion through a combination of permanent cuts to a number of federal agencies and one-time reductions to other government programs, such as Pell grants and some agriculture subsidies.

Republicans are balking at many of the temporary cuts because they will not permanently reduce the size of government.

Even if the chairmen of the House and Senate appropriations committees can agree on a package of cuts, and conservative House members decide to go along with the plan, there may not be enough time to approve it before the deadline.

According to a House rule Boehner put in place this year, no bill can come to a vote until members have had three days to read it — leaving almost no time for the Senate to act if the House could not approve its version until late Friday or over the weekend.

House Republicans huddled late Monday and, according to a GOP aide, gave the speaker an ovation when he informed them that he was advising the House Administration Committee to begin preparing for a possible shutdown. That process includes alerting lawmakers and senior staff about which employees would not report to work if no agreement is reached.

Boehner’s offer of another stopgap bill comes at a significantly higher cost than the $2 billion in cuts per week that accompanied the two most recent short-term funding plans. Also, Republicans are attaching some policy prescriptions to the one-week measure, including one that would prohibit federal funds going toward any abortion services in the District.

The issue will come to a head Tuesday at a White House gathering of Obama, Boehner, Reid, Senate Appropriations Committee Chairman Daniel K. Inouye (D-Hawaii) and House Appropriations Committee Chairman Harold Rogers (R-Ky.).

“The president has made clear that we all understand the need to cut spending, and significant progress has been made in agreeing that we can all work off the same number,” White House press secretary Jay Carney told reporters Monday.

Republicans and Democrats are eager to avoid a shutdown in part because neither side thinks it will be able to claim political advantage. In a new Washington Post poll, 37 percent say they would fault the Obama administration for a partial federal shutdown. The same number would blame the Republicans in Congress.

Those figures are nearly the same as in late February, despite five weeks of fierce negotiations and positioning on the issue.

This is a change from the government shutdowns in the mid-1990s. In late 1995, 46 percent of voters said they would blame then House speaker, Newt Gin­grich (R-Ga.), if the government shut down, and 27 percent would blame President Bill Clinton.

The new numbers also indicate growing disillusionment among Republicans. While 81 percent of Republicans say they think Obama is “just playing politics” with the budget (up from 70 percent five weeks ago), 40 percent of all Republicans see the GOP in Congress as posturing on the budget — a 13-point increase.

Staff writers Perry Bacon Jr., Felicia Sonmez and Ed O’Keefe contributed to this report.

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