Washington (CNN) -- A day after meeting separately with President Barack Obama, the Senate's top Democrat and top Republican continued to spar Tuesday over whether increased tax revenue should be part of a deficit reduction agreement.
Senate Minority Leader Mitch McConnell, R-Kentucky, told reporters that an insistence by Obama and Democrats to raise tax revenue "in the middle of an economic slowdown" was blocking progress on a deal demanded by Republicans in return for their support to raise the federal debt ceiling.
"We think it's a job-killing step that shouldn't be taken, and Republicans are not interested in going in that direction," McConnell said.
His Democratic counterpart, Senate Majority Leader Harry Reid of Nevada, said McConnell's stance shows Republicans are more interested in protecting the wealthy and special interests than spreading the burden of deficit reduction across all of American society.
"Republicans should be prepared to accept the hard truths we face and do the right thing to protect the middle class instead of millionaires and billionaires," Reid told reporters.
Despite the rhetoric, the White House believes a "significant" deal remains possible this year, and Press Secretary Jay Carney told reporters Tuesday that Obama will meet Wednesday with Senate Democrats to further discuss the issue. No additional meetings with Republicans have been scheduled, Carney said, while McConnell said talks will continue.
Monday's meetings came after bipartisan talks led by Vice President Joe Biden concluded last week without an agreement, causing Obama to get directly involved.
With an August 2 deadline looming to increase the federal debt ceiling or face possible default on debt obligations, pressure is mounting to reach a deal that would prevent market jitters and corresponding harm to the still-recovering economy.
Both McConnell and Reid expressed concern for protecting the economy, although from different perspectives.
To McConnell and other Republicans, any kind of an increased tax burden now -- even in the form of eliminating loopholes and subsidies rather than raising tax rates -- would deter economic recovery.
"The last thing you want to do to an ailing economy is to saddle it with more taxes," conservative Sen. Jon Kyl, R-Arizona, told reporters. "Getting economic recovery is more important than some ideological attachment to raising taxes."
Reid, however, said linking a deficit reduction deal to the needed debt ceiling increase is a dangerous and ill-advised maneuver by Republicans. Failing to raise the debt ceiling would put the United States in default on its obligations and have a "catastrophic" impact on the economy, he said.
Republicans walked away from the Biden-led talks because they opposed eliminating tax subsidies for oil companies and tax breaks for people who own corporate jets, he added.
"Republicans' priorities are clear. They're also dead wrong," Reid said on the Senate floor.
Reid also criticized Republican Sen. Jim DeMint of South Carolina for threatening political reprisals against GOP any senators who vote to raise the debt ceiling without an acceptable package in return, noted he "threatened that any Republican who votes to avert a default crisis will be 'gone' -- voted out in a wave of Tea Party anger."
"This kind of inflammatory language is irresponsible," Reid said of DeMint. "There is simply too much at stake."
On Monday, Kyl confirmed that disagreement over the tax revenue issue ended the Biden-led talks in which he took part with House Majority Leader Eric Cantor, R-Virginia.
"The primary problem there was the insistence by the Democratic negotiators that Republicans agree to tax hikes, something which we think would be inimical to economic growth," Kyl said, later adding that "the White House's insistence that this had to be a condition to approving the reductions in spending that we had been talking about made it impossible for us to go forward at that time."
The Biden-led talks made progress on identifying spending cuts -- including defense spending -- and laying out a blueprint for possible reforms to entitlement programs such as Medicare and Medicaid, the government-run health insurance for senior citizens, the disabled and the poor.
While differences remain on specifics, the ability of the two sides to acknowledge the need to include such politically sensitive issues was considered a positive development that heralded the possibility of continued progress.
However, the tax revenue issue now stands as the main obstacle to an agreement, with both sides showing little indication of easing their positions.
At the heart of the GOP resistance is a bedrock principle pushed by anti-tax crusader Grover Norquist against any kind of tax increase at all. A pledge pushed by Norquist's group, Americans for Tax Reform, against any tax increases has been signed by more than 230 House members and 40 senators, almost all Republicans.
Norquist and his supporters want to shrink the federal government and believe any new revenue would enable continued government growth.
However, some Republicans, including conservative Sens. Tom Coburn of Oklahoma and Lindsey Graham of South Carolina, have expressed support for increased tax revenue as part of a deficit reduction deal, and the Senate recently supported ending ethanol subsidies -- which would increase revenue.
Tax loopholes targeted by Democrats include oil and gas subsidies, as well as some write-offs for people earning more than $500,000 a year. In addition, Democrats call for ending Bush-era tax cuts for people earning more than $250,000 a year, which Republicans steadfastly reject.