President Barack Obama met with the U.S. Congress’ top Republican, House of Representatives Speaker John Boehner on Sunday in search of a deficit-reduction package that would prevent substantial spending cuts and tax increases from going into effect on January 1.

Sunday’s meeting at the White House marked the first face-to-face debt discussions between President Obama and Speaker Boehner in nearly a month.  After their first encounter, the White House and Mr. Boehner made opening bids on a debt-reduction package that would avert the so-called fiscal cliff.  Each side rejected the other’s offer as unacceptable, a stance that lawmakers voiced on U.S. television only hours before the Obama-Boehner meeting.

“Unfortunately, what we see out of the president is ‘my way or the highway’," said Republican Congressman Jeb Hensarling. Appearing on ABC’s This Week program, Hensarling said the stumbling block to a deal is Obama’s insistence on higher tax rates.

“No Republican wants to vote for a tax-rate increase," he said.

But some Republicans say they would accept higher taxes on the wealthy in return for reforms to programs that provide health care and income for retirees.  Senator Tom Coburn also appeared on This Week. “Will I accept a tax increase as part of a deal to actually solve our problems?  Yes," he said.

Coburn insists tax hikes alone will not solve America’s trillion-dollar annual federal deficit. But just as many Republicans dislike tax hikes, many Democrats are reluctant to reform programs relied on by retirees, as well as the poor and vulnerable.

Democratic Congressman Raul Grijalva said it is unjust to ask middle and lower-income Americans to bear the burden of deficit reduction, after a decade of rising income inequality between the wealthy and everyone else. “And now we are being asked to go back to the same people who have endured this crisis, and ask them to pay up again.  No," he said.

President Obama has urged Congress to extend existing tax breaks for all income under $250,000 a year, an idea that has the backing of Democratic Senator Debbie Stabenow.

“At the end of this year, if the House of Representatives does not pass the middle-class tax cut, we are going to see middle-class families across this country paying at least $2,200 more in taxes they cannot afford," he said.

If lawmakers do not reach a debt agreement, federal taxes will rise for all income groups, and domestic and military spending will be cut across the board beginning January 1.  Economists believe an austerity jolt of that magnitude could send the U.S. economy back into recession.