Polling has consistently shown most Americans back the president, who insists wealthy Americans must pay more, rather than Boehner and his Republican colleagues, who have balked at tax rate hikes and demanded spending cuts and entitlement program reforms.

A new CNN/ORC International survey released Thursday showed that just over half of respondents believe Republicans should give up more in any solution and consider the party's policies too extreme.

The two sides seemingly had made progress earlier this week on forging a $2 trillion deficit reduction deal that included new revenue sought by Obama and spending cuts and entitlement changes desired by Boehner.

The president's latest offer set $400,000 as the income threshold for a tax rate increase, up from his original plan of $250,000. It also included a new formula for the consumer price index applied to some entitlement benefits, much to the chagrin of liberals.

Called chained CPI, the new formula includes assumptions on consumer habits in response to rising prices, such as seeking cheaper alternatives, and would result in smaller benefit increases in future years.

Statistics supplied by opponents say the change would mean Social Security recipients would get $6,000 less in benefits over the first 15 years of chained CPI.

Liberal groups sought to mount a pressure campaign against including the chained CPI after news emerged this week that Obama was willing to include it, calling the plan a betrayal of senior citizens who had contributed throughout their lives for their benefits.