Senators who cut short holiday vacations to return to a deadlocked Washington offered varying degrees of optimism Friday on the potential of a fiscal cliff deal emerging from an afternoon meeting between President Barack Obama and congressional leaders.

Sen. Chuck Schumer, speaking on NBC's "Today" show, said he was "a little more optimistic today" about reaching a deal that would avoid the automatic tax increases and spending cuts that will go into effect at the end of the year. Both Republicans and Democrats have sounded increasingly downbeat on the chances of finding a solution before the effects of the cliff kick in.

"Sometimes it's darkest before the dawn," the New York Democrat said, pointing to renewed engagement from Republicans, including Senate Minority Leader Mitch McConnell and House Speaker John Boehner. McConnell and Boehner, along with Senate Majority Leader Harry Reid and House Minority Leader Nancy Pelosi, will meet with Obama in the Oval Office at 3 p.m. ET Friday.

"The fact that (Boehner's) come back and the four of them are at the table means to me we could come up with some kind of agreement that would avoid the main parts of the fiscal cliff, particularly taxes going up on middle-class people," Schumer said.

Sen. Olympia Snowe, R-Maine, said on CNN's "Starting Point" that a deal must originate between Obama and the four congressional leaders for Americans' confidence to be restored in the federal government.

"It's got to start with the leaders and the president at the White House this afternoon. Hopefully they'll agree to a framework," said Snowe, who is retiring. She told CNN's Ali Velshi that the Democrat-controlled Senate would then vote on any potential measure before sending it to the Republican-held House of Representatives.

"I hope the speaker can get this job done before the end of this year and not defer it to next year," she continued. "We've got to demonstrate we have some capacity left to make decisions in Washington on these very significant issues for the country."

Schumer's and Snowe's optimism was countered by Republican Sen. Bob Corker of Tennessee, who downplayed the importance of Friday's meeting on CBS "This Morning."

"This afternoon's meeting feels too much to me like optics to make it look like we're doing something," Corker said. "Let me just say one more time: This is a total dereliction of duty at every level. I've been very surprised that the president has not laid out a very specific plan to deal with this, but candidly Congress could have done the same, and I think the American people should be disgusted."

He predicted the meeting between Obama and the lawmakers would result in a "kick-the-can-down the road" solution, meaning larger questions on tax increases and spending cuts would be put off until next year.

Asked whether lawmakers understood the importance of striking a fiscal cliff deal before the end of the year, Democratic Sen. Debbie Stabenow of Michigan said her colleagues in the Senate did -- but that a different story was playing out on the other side of Capitol Hill.

"We're having a lot of very important, very good, positive conversations between Democrats and Republicans (in the Senate)," she said on "Starting Point."

"The tough part is in the House. They have taken this very extreme position about protecting the wealthiest Americans at all costs, even holding middle-class families hostage to do it. And that really isn't rhetoric. We're seeing it over and over again."