Negotiations to end the government shutdown and raise the nation's debt ceiling accelerated Saturday when the Senate's top Republican and top Democrat entered into direct talks to negotiate a final deal.

Senate Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., met early Saturday to begin work on a compromise and hope to have at least the framework for a deal in place before Wall Street opens for business Monday, just three days before the government would hit its borrowing limit and default on the nation's $16.7 trillion debt.

Reid described talks with McConnell as preliminary, but he sounded hopeful that they could bare fruit.

“We are negotiating,” Reid said at a Capitol Hill news conference. “We are not locked in stone.”

Sen. Lamar Alexander, R-Tenn., who along with Sen. Charles Schumer, D-N.Y., helped facilitate the Reid-McConnell negotiations, said finding a consensus solution to the fiscal impasse was now in the hands of the chamber’s two leaders. “In the end, Sen. McConnell and Sen. Reid have to come up with a recommendation for us about how to open the government, how to pay our bills by raising the debt limit and how to reduce the debt.”

Senate Democrats' primary proposal to raise the debt ceiling — raising it until after the 2014 elections — died on the floor Saturday after Republicans denied Democrats the votes they needed to reach the 60-vote threshold and advance. That proposal would allow a borrowing limit increase of $1 trillion. Even if the Senate passed it, the Republican House would likely have rejected it.

The center of gravity in the twin battles over the government shutdown and debt ceiling has shifted from the Republican House to the Democratic Senate. President Obama rejected the House GOP’s latest debt and spending deal, opting instead to negotiate with Senate Democrats and Senate Republicans who are also eager to end the shutdown, now in its 12th day.

Senate Democratic leaders were headed to the White House Saturday for more discussions.

Both Reid and the administration have shot down a brewing bipartisan compromise engineered by Sens. Susan Collins, R-Maine, and Joe Manchin, D-W.Va. Their framework included some Obamacare reforms and would have immediately reopened the government while providing a short-term debt ceiling increase to allow for broader negotiations. Senators remain engaged in bipartisan discussions, but it appears a deal is likely to be dependent on Reid and McConnell, with Obama’s sign-off.

"I think there's a reason to believe that ultimately, we'll work it out,” Senate Majority Whip Dick Durbin, D-Ill., said.

Reid declined to provide details on what he and McConnell discussed Saturday morning. But he signaled that Democrats would seek to restore the spending cuts achieved through sequestration as a part of any final deal. Senate Republicans, meanwhile, remain committed to protecting the sequester cuts in any final agreement.

Other issues being discussed are how long the temporary spending bill would leave the government open. Senate Republicans want a yearlong deal that would immediately reopen the government, but only a short-term increase in the debt ceiling. Democrats are willing to accept a short-term deal on government spending because they want time to negotiate with Republicans over the sequester-level spending cuts. But they want the debt ceiling raised for a year, until after the 2014 elections.

As McConnell seeks to negotiate a deal acceptable to a broad array of Senate Republicans, the Kentuckian must also be mindful of striking a deal that the House GOP won't reject so close to deadline. Reid made clear that it is McConnell’s “responsibility” to communicate with House Speaker John Boehner, R-Ohio, on that front.

House Republicans remain committed to their latest offer despite Obama's rejection and the loss of their lead in budget talks. The House Republican proposal would lift the debt ceiling for six weeks to allow for broader negotiations, including on a spending bill to end the government shutdown.

House Republicans are in this weakened position because they cannot unify around any other legislation beyond what they’ve offered thus far that might outflank the Senate and force Obama to steer the negotiations back to them. Meanwhile, Senate Republicans had grown impatient with their House counterparts’ tactical inflexibility, not to mention their insistence on maintaining the government shutdown and willingness to flirt with approving a “clean” debt ceiling bill.

House Republicans concede that they are worried about being jammed at the eleventh hour by bipartisan Senate agreement, and they are aware that their leadership might have no choice but to put such a bill on the floor. But House Republicans warn that they would not provide the votes for an unacceptable, even if they are up against the Thursday deadline to raise the debt ceiling.

House Homeland Security Chairman Michael McCaul, R-Texas, said his caucus his concerned that Senate Republicans could end up agreeing to a bad deal. "I don't know what they're going to come up with. It's going to have to be a bipartisan agreement.”

Examiner White House Correspondent Susan Crabtree contributed to this report.