"He's going to get his wish. I believe we're going to be raising taxes, and not just on the top earners," DeMint, who is leaving the Senate to become president of the Heritage Institution think tank, said in an appearance on "CBS This Morning."
DeMint said a tax increase would amount to a "political trophy" for Obama but said it would be bad for the country.
"The president's proposal is not a plan, it's not a solution," he said.
There is increasing concern about a Dec. 31 deadline to stop the expiration of Bush-era tax cuts and the start of across-the-board spending cuts that are the result of Washington's failure to complete a deficit-reduction deal last year. Even if an agreement can be reached, the halting pace of negotiations is jeopardizing chances that it could be written into proper legislative form and passed through both House and Senate before the new Congress convenes on Jan. 3.
"I do have an increasing concern that the speaker ... is trying to string this out until Jan. 3 because that's when he would be re-elected as speaker," said Rep. Chris Van Hollen of Maryland, top Democrat on the House Budget Committee. "And I think he's nervous that if he can't get a majority of his House Republican members to support a reasonable agreement that that could put his speakership election in jeopardy. And so that might cause him to try and string these talks" along.
Republicans say it's Democrats who are dragging out the talks.
"In the past 48 hours, the president has not been negotiating in good faith in my opinion," said Rep. Pat Tiberi, R-Ohio, who said he was increasingly pessimistic that a deal could be reached.
Associated Press writers Alan Fram and Nyia Hawkins contributed to this report.
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