The Quinnipiac University national survey showed 65% of registered voters support higher taxes on the wealthy, though Republican respondents were opposed, 53% to 41%.
Also, a Washington Post/Pew Research Center survey released Tuesday showed 53% of respondents would blame Republicans for failure to reach a deal, compared with 27% who would blame Obama. A CNN/ORC International poll released last week showed 45% would blame congressional Republicans compared with 34% who would hold Obama responsible.
Retiring Republican Rep. Steve LaTourette of Ohio told CNN that he sensed a shift in the House GOP approach during a conference meeting on Wednesday.
"The sense was that there's a growing number of folks in our party that are saying, 'You know what, the president has won this round relative to the rates, but we need to you to sit down and get the second half of the deal and that's the spending,'" LaTourette said.
Even conservatives such as Oklahoma Sen. Tom Coburn and Louisiana Gov. Bobby Jindal acknowledge the obvious -- that taxes on the wealthy are going up despite opposition by Republicans.
"Whatever deal is reached is going to contain elements that are detrimental to our economy," Jindal wrote Thursday in an opinion piece published by Politico. "Elections have consequences, and the country is going to feel those consequences soon."
At the same time, Jindal wrote, "Republicans certainly should fight to at least get something done that will matter."
"At present, any reading of the headlines over the past week indicates that Republicans are fighting to protect the rich and cut benefits for seniors," he added. "It may be possible to have worse political positioning than that, but I'm not sure how."
Coburn, a well-known fiscal hawk, told MSNBC on Wednesday that he would support higher tax rates on wealthier Americans as part of a broader deal to avoid the fiscal cliff and broader deficit crisis.
"I know we have to raise revenue," Coburn said. "I don't really care which way we do it. Actually, I would rather see rates go up than do it the other way, because it gives us a greater chance to reform the tax code and broaden the base in the future."
Despite the public stance softening of some Republicans in each house, signs point to a continuing standoff for now.
Senate Republican leader Mitch McConnell warned Thursday that his party will continue to use the federal debt-ceiling issue as leverage to extract concessions on spending cuts from Democrats, a tactic that Obama opposes.
"The only way we ever cut spending around here is by using the debate over the debt limit to do it," McConnell said in response to Obama's call for removing the issue from political negotiation.
At the White House, spokesman Jay Carney said such brinksmanship over a matter involving a possible unprecedented government default was opposed by the business community and the American public.
"I can't imagine they would want to do that," he said of Republicans.
After meeting with his conference Wednesday, Boehner told reporters that the rich will be paying more, but he still hoped to limit any increase to ending tax deductions and loopholes rather than Obama's demand for higher rates.
Obama, however, continued to insist that Republicans must agree to higher tax rates for the wealthiest Americans before working out a broader deficit reduction deal.
The president demands that the House immediately pass a measure already approved by the Senate to extend tax cuts from 2001 and 2003 on income up to $250,000 for families.
He contends that both Democrats and Republicans agree that the 98% of American families making less than $250,000 a year should avoid a tax hike when the lower rates from the Bush administration expire on December 31. They call for the House to guarantee that outcome by passing the Senate measure now.
Once that happens, Obama and Democratic leaders promise, they will work out compromises on other spending cuts sought by Republicans to reduce the deficit, such as reforms to the Medicare and Medicaid entitlement programs.
The broader deficit reduction plan from the president would increase tax revenue by $1.6 trillion over 10 years through the higher rates on the wealthy as well as closing loopholes, limiting deductions, raising the estate tax rate to 2009 levels and increasing tax rates on capital gains and dividends.
Under it, $500 billion would come from limiting itemized tax deductions and other benefits for high-income earners. A 28% limit on deductions would apply to families earning more than $250,000 and individuals making more than $200,000, according to the White House.
The Obama plan also includes $50 billion in stimulus spending for programs intended to create jobs, such as repairing roads and bridges.
In response, House Republicans offered a plan that they said could reduce federal deficits by $2.2 trillion over 10 years.
The GOP proposal includes $800 billion from tax reform, $600 billion from Medicare reforms and other health savings and $600 billion in other spending cuts, House Republican leadership aides said. It also pledges $200 billion in savings by revising the consumer price index, a measure of inflation.