Appearing on the same show, Republican Sen. John Thune noted the meeting scheduled later Friday at the White House, saying "it's encouraging that people are talking."
But Sen. Bob Corker, R-Tenn., predicted that "the worst-case scenario" could emerge from Friday's talks.
"We will kick the can down the road," he said on "CBS This Morning."
"We'll do some small deal and we'll create another fiscal cliff to deal with the fiscal cliff," he said. Corker complained that there has been "a total lack of courage, lack of leadership," in Washington.
If a deal were to pass the Senate, Boehner would have to agree to take it to the floor in the Republican-controlled House.
Boehner discussed the fiscal cliff with Republican members in a conference call Thursday and advised them that the House would convene Sunday evening. Rep. Tom Cole, R-Okla., an ally of the speaker, said Boehner told the lawmakers that "he didn't really intend to put on the floor something that would pass with all the Democratic votes and few of the Republican votes."
But Cole did not rule out Republican support for some increase in tax rates, noting that Boehner had amassed about 200 Republican votes for a plan last week to raise rates on Americans earning $1 million or more. Boehner ultimately did not put the plan to a House floor vote in the face of opposition from Republican conservatives and a unified Democratic caucus.
"The ultimate question is whether the Republican leaders in the House and Senate are going to push us over the cliff by blocking plans to extend tax cuts for the middle class," White House communications director Dan Pfeiffer said. "Ironically, in order to protect tax breaks for millionaires, they will be responsible for the largest tax increase in history."
Boehner, McConnell, Reid and House Democratic Leader Nancy Pelosi are all scheduled to attend Friday's White House meeting with Obama. Vice President Joe Biden will also participate in the meeting, the White House said.
Associated Press writers Alan Fram, Charles Babington and David Espo contributed to this report.