He blamed what he called "an absolutist position" by Republicans such as Boehner in opposing the Democratic demand for deficit reduction to include both spending cuts and increased tax revenue.
Carney characterized such opponents as saying "no way, no how" to more revenue even though "the public ultimately supports that approach, even though there are voices in the Republican Party who believe that's the right approach to take."
"We'll see if there are enough members -- Republican members -- of the caucus of common sense to allow for progress to be made," he added.
Compromise is needed to prevent a recurrence of political showdowns like those from Obama's first term that contributed to a downgrade of the U.S. credit rating and sluggish economic recovery.
In an interview broadcast Wednesday on ABC, Obama warned such agreement may prove unattainable.
"Right now what I'm trying to do is create an atmosphere where Democrats and Republicans can go ahead and get together and try to get something done," he said of his so-called charm offensive that has included a dinner with GOP senators, lunch with House leaders and the meetings with both party caucuses in Congress. "But ultimately it may be that the differences are just too wide."
Last week, the president invited a dozen Republican senators to dinner and hosted lunch with the top members of the House Budget Committee to launch what reporters dubbed the charm offensive.
His outreach continued this week with visits to the Capitol on Tuesday, Wednesday and Thursday, concluded by his meeting with House Democrats after the talks with Senate Republicans.
Meanwhile, both the House and Senate budget committees began working this week on separate spending proposals for fiscal year 2014 that reflected the deep partisan divisions in Washington over tax and funding issues.
Republicans led by their conservative base seek to shrink the size and cost of government, opposing any new tax revenue while pushing for spending cuts and lower tax rates that they say will spur more economic growth.
After agreeing in January to allow the higher tax rates on top income earners, Republican leaders say they oppose any further steps to raise taxes.
Obama and Democrats say they want to protect Medicare, Medicaid and Social Security, and that comprehensive deficit reduction must include increased taxes on wealthy Americans to prevent the burden of austerity steps from shifting too much to the middle class, the elderly and other vulnerable demographics.
The Senate budget proposal for 2014 by Budget Committee Chairwoman Patty Murray, D-Washington, called for a mix of increased tax revenue and spending cuts to reduce deficits by about $1.9 trillion over 10 years.
It would increase revenue by about $975 billion by eliminating and curtailing tax breaks and loopholes for wealthy Americans and corporations. It would also cut spending by an estimated $975 billion: $493 billion in domestic spending; $240 billion in defense spending; and $242 billion in interest savings.
The proposal included a $100 billion economic stimulus package for road and bridge repairs, as well as worker training, that Murray said would be paid for by curtailing tax breaks for high-income households and corporations.
However, the Senate plan avoided significant changes to popular entitlement programs such as Medicare and Medicaid, which are major drivers of federal deficits.
Obama will introduce his own budget proposal next month, and the president and Democrats concede their approaches would not eliminate annual deficits, as sought by Republicans, but instead reduce them to what they say are manageable levels.
Republicans call such an approach inadequate, insisting that government has become too large and costly to ensure needed economic growth.
House Budget Committee Chairman Paul Ryan, R-Wisconsin, proposed a conservative spending plan for 2014 that he said would eliminate the annual deficit in a decade without raising taxes.
It calls for cutting $5 trillion from projected spending increases in the next 10 years while lowering tax rates and getting rid of most of Obama's signature legislation of his first term -- the 2010 health care reform law.
Ryan also revived his proposal to reform Medicare, the health care program for senior citizens that is considered the biggest driver of rising federal deficits as costs increase and more Americans become eligible.
The idea was a major issue in last year's presidential election, in which Ryan was the vice presidential candidate on the GOP ticket that lost to Obama.
His Medicare revision calls for offering senior citizens a choice between traditional fee-for-service Medicare and a premium support system that would provide a fixed government payment to help them buy private health insurance. The plan would take effect in 2024 to exempt people 55 and older today.
By clearly staking out positions in their budget proposals, Obama and Congress appear intent on trying to avoid the crisis-driven brinksmanship of the past four years.
However, the familiar, partisan nature of the budget plans illuminated the continuing political division that the public blames for legislative dysfunction.