WASHINGTON – After weeks of arguing, Republicans and Democrats on Capitol Hill began negotiations Wednesday on a possible budget agreement that would slash federal spending by as much as $33 billion and avert a government shutdown.

“We’re all working off the same number now,” Vice President Joe Biden told reporters after meeting with Senate Democratic leaders at the Capitol on Wednesday evening. “Obviously, there’s a difference in the composition of that number — what’s included, what’s not included. It’s going to be a thorough negotiation.”

If approved, the deal would be the largest single-year budget cut in U.S. history.

Lawmakers in both parties are eager to reach a compromise to fund the government through September, the end of the fiscal year, and end the stopgap spending resolutions that have kept Washington operating a few weeks at a time since fall. The current short-term measure will expire April 8, and congressional leaders have said they don’t want to pass another one.

The two sides have already agreed on $10 billion in cuts; now, the House and Senate appropriations committees are searching for an additional $23 billion to extract from the budget, according to lawmakers and aides from both parties.

“We’re going to try to find some common ground,” House Appropriations Chairman Harold Rogers, R-Ky., told reporters. “It’s going to take some time. … But the leadership has said for us to get started.”

Congressional leaders cautioned that no final deal has been reached. The talks could break down over disputes about how much to cut and from where.

Some conservative House Republicans — led by freshmen who came to Washington on a promise to shrink the government — have said they would reject any proposal that falls short of the $61 billion in reductions the House approved on a party-line vote last month. Senate Democrats immediately rejected it.

The progress in the negotiations came on the eve of a planned rally by tea party activists on the Capitol lawn, with leaders of the conservative movement calling for no compromise with President Obama and the Democratic-controlled Senate.

House Republicans fear a significant number of their rank-and-file lawmakers could view a compromise with Democrats as a retreat. If Boehner loses the support of two dozen or more of his GOP colleagues, he could turn to moderate Democrats for support on a final spending package.