In the Republican video response, Senator Jon Kyl of Arizona said that “Republicans have tried to work with Democrats,” to raise the debt ceiling, “but we need them to work with us.”

In an effort to send a message, House Republicans plan to allow a symbolic vote Saturday on Mr. Reid’s plan to show that it cannot clear the House.

In the Senate, Democrats filed a motion on Friday that started debate, running down the procedural clock while Republicans expressed their opposition. The first vote on overcoming the procedural hurdles would come early on Sunday. Unless the Democrats can win over enough Republicans to cut off debate and move to approve the Reid bill or some variant, the Republicans would be forced to hold the floor continuously, awaiting some kind of deal.

Many members of the Senate are hoping Mr. Reid and Senator Mitch McConnell of Kentucky, the Republican leader, can strike an agreement that can attract members of both parties to approve a measure that could be sent back to the House. And some Republicans began to encourage a compromise, with a spokeswoman for Senator Scott Brown, Republican of Massachusetts, saying he could back “a Republican bill, or a Democrat bill — it doesn’t matter” as long as it cuts spending, does not raise taxes and avoids default.

But Mr. Reid contended Friday that he was not finding a receptive audience for compromise in Mr. McConnell. “They are not negotiating,” he said. Republican aides said they expected talks to begin, but they wanted to make sure that the White House was part of the bargaining.

The main legislative focus was on the search for an acceptable “trigger” that would guarantee that no second installment of a debt limit increase would be provided without consideration of further spending cuts or program policy changes. Democrats say they are willing to allow a new special committee to consider sweeping deficit reduction and tax policy changes but want the debt limit increase assured; Republicans do not want President Obama to get a second increase without meeting some standard, which would be passage of a balanced budget amendment through Congress under the new House plan.

A new Congressional committee would also have to produce $1.6 trillion or more in savings and win approval of that plan. In many other respects, the plans offered by House Republicans and Senate Democrats are quite similar, and the savings — aside from how those related to winding down the wars in Iraq and Afghanistan wars are calculated — are also similar, leading many on Capitol Hill to believe a deal could be reached if lawmakers would draw back from their hardening positions.