WASHINGTON — Senators Harry Reid and Mitch McConnell on Saturday began last-ditch negotiations on reopening the government and raising the debt ceiling as talks between House Republicans and the White House collapsed, dashing hopes for a quick resolution to the political crisis that has paralyzed the government.

The dead end with the House, coming just five days before the nation reaches its borrowing limit and faces the possibility of a crippling financial default, has left Republicans on Capitol Hill with no easy options.

“No deal,” Representative Paul D. Ryan, the chairman of the House Budget Committee, said as he left a meeting with fellow Republicans in the Capitol.

There is now little doubt that any deal to reopen the federal bureaucracy would have to come from the Senate, where Mr. Reid, the majority leader, and Mr. McConnell, the minority leader, sat down face to face on Saturday morning for the first time since July. The meeting, which both sides described as a constructive if highly preliminary step toward talks that would continue throughout the weekend, was an indication of just how urgent the situation had become.