President Obama huddled Saturday afternoon with Senate Majority Leader Harry Reid and other Democratic leaders who left the meeting saying Democrats remain united in their position of agreeing to negotiate on GOP priorities only after the government is reopened and the debt-ceiling is raised.

The rare Saturday intra-party meeting at the White House came as the focus shifts to the Senate to find a way to break through the budget impasse.

The White House earlier Saturday rejected an offer by House Republicans to increase the debt limit for a short period to allow more time for negotiations to take place, sparking an angry response from several GOP members frustrated by another stall just when they believed a deal might be in reach.

The focus of the debate then shifted to the Senate, and Reid reported that he had begun talking with Minority Leader Mitch McConnell, R-Ky., early Saturday. While Reid said there was no progress to report, he said he viewed the conversations with the GOP leader as a positive, hopeful sign.

After the White House meeting, however, Senate Democrats said they would not be willing to make any concessions to Republicans until the leverage is gone -- after the government re-opens and and the debt-ceiling is raised.

Democrats also accused Republicans of lacking a coherent negotiating position.

"The President and the leaders compared notes and reviewed a number of the options raised in meetings over the past few days," said a Senate Democratic leadership aide. "Their conclusion was that while Democrats remain united, Republicans have yet to coalesce behind a clear negotiating position."

"The President and the leaders agreed that talks between Senate Democratic and Senate Republican leaders should continue in the coming days, but Democrats' position remains the same: Democrats are willing to negotiate on anything Republicans want to discuss as soon as we reopen the government and pay our bills," the aide said.

Earlier Saturday, the Senate, as expected, voted down a procedural motion on a clean continuing resolution and there was little indication from the White House of any progress.