The top Democrat and Republican in the Senate emerged from a meeting at the White House Friday evening to say they are hopeful they can strike a last-minute deal to avert the tax increases and spending cuts looming in less than four days.

“What we come up with is going to be imperfect,” Senate Majority Leader Harry Reid, Nevada Democrat, told his colleagues on the chamber floor.

He, Sen. Mitch McConnell, House Speaker John A. Boehner and House Minority Leader Nancy Pelosi met with President Obama for a little more than an hour, and the two Senate leaders said they will try to write a deal now, after the House has stalemated.

Speaking at the White House, Mr. Obama said he is “modestly optimistic” that Mr. Reid and Mr. McConnell can work out an agreement, saying his meeting with congressional leaders had been a “good and constructive discussion.”

But the president said he also made clear that if their efforts fail, he expects Mr. Reid to bring up a Democratic package that extends tax cuts for families with income under $250,000, provides extended unemployment insurance benefits for 2 million Americans and lays out a framework for future deficit reduction.

“I believe such a proposal could pass both houses with bipartisan majorities, as long as those leaders allow it to actually come for a vote,” Mr. Obama said. “We should let everybody vote. That’s the way this is supposed to work.”

The president sounded a note of skepticism about the Senate negotiations, saying “the hour for immediate action is here” and accusing lawmakers of dragging their feet.

“Given how things have been working in this town, we always have to wait and see until it actually happens,” he said of the last-ditch talks. “So if we don’t see an agreement between the two leaders in the Senate, I expect a bill to go on the floor” based on the president’s priorities.

Neither the House or Senate will be in session Saturday but both will be here Sunday — the Senate reconvening after a daylong break, and the House returning to Washington after a 10-day vacation.

Mr. McConnell and Mr. Reid both sounded optimistic they can try to bridge the gap, though that doesn’t assure a deal’s passage.

Mr. Boehner’s office said the speaker insisted the Senate act on the bills the House has already passed, and he said if the upper chamber does find bipartisan agreement, the House will then hold a vote on it.

That was a key concession for Senate Democrats, who had insisted Mr. Boehner agree to hold a vote in the whole House on whatever plan emerges from the Senate.

That could help Democrats get around a vocal conservative Republican voting block in the House that scuttled Mr. Boehner’s last proposal a week ago.

Still, Mr. Boehner’s offer was only to take the bill to the House floor — it did not guarantee an up-or-down vote.

It’s also unclear whether Mr. Boehner would allow Mr. Obama’s plan to come to the floor should the Reid-McConnell Plan C fail to materialize.

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