* No follow-up talks set for Obama, Republicans
* Five weeks until Aug. 2 deadline
* Republicans want to separate tax debate from debt talks (Adds Boehner comments, paragraphs 11-13)
WASHINGTON, June 28 (Reuters) - U.S. Democrats and Republicans on Tuesday showed no sign of resolving an impasse over taxes that has stalled budget negotiations and could threaten the country's top-notch credit rating.
The two sides will not make progress on a deal to extend the U.S. borrowing authority as long as Democrats continue to push for tax increases, the Senate's top Republican said.
"The path forward ... seems to be blocked by the insistence on raising taxes in the middle of an economic slowdown," Senate Republican leader Mitch McConnell said at a news conference, one day after meeting with President Barack Obama.
Democrats accused Republicans of protecting perks for the wealthy at the expense of efforts that would allow the country to avoid a catastrophic default.
"Republicans walked away from the negotiating table to save tax breaks for corporate jets," Senate Democratic leader Harry Reid said on the Senate floor.
The Treasury Department has warned it will run out of money to pay the country's bills if Congress does not raise the $14.3 trillion debt limit before Aug. 2.
Even if a deal is reached soon, lawmakers will need time to turn the proposal into legislative language, sell it to their constituents, and pass it through the House of Representatives and the Senate -- a process likely to take weeks.
"The last thing anyone wants is to have some kind of agreement down at the White House behind closed doors parachuted in and say, 'Well, representatives and senators, you've got three days to think this over and vote on it.' That's wrong and we're not going to allow that," said Republican Senator Jon Kyl, a participant in discussions that collapsed last week over tax increases.
Financial markets have shown little sign of concern so far, but that could change as the Aug. 2 deadline approaches.
DEAL NOT LIKELY SOON
A deal does not appear likely any time soon. Obama has met separately with McConnell and House Speaker John Boehner, the top Republican in Washington, but no follow-up meetings have been set, aides said.
Boehner said he has told Obama that tax increases would not pass through Congress.
"No tax increases. Zero," Boehner said in an interview with Fox News Channel. "There are no votes in the Congress -- in the House or the Senate -- there's not a majority to raise taxes on anyone. So tax increases are off the table."
Boehner said he had a "very honest conversation" with Obama but said Democrats were not "dealing with reality" on taxes.
Obama will meet with Senate Democrats on Wednesday.
Aides from both parties suggested there would be little reason to hold meetings as long as the two sides remain at odds over tax increases.
Democrats say the $1.5 trillion to $2 trillion in spending cuts that the two sides have tentatively identified must be augmented by $400 billion in new tax revenue over the coming 10 years. That money would come by closing a range of tax breaks for hedge-fund managers, private jets and specific business sectors. [ID:N1E75R1CD]
"We believe there is the opportunity here for a substantial compromise on a significant deficit reduction agreement that is done in a way that's balanced," White House spokesman Jay Carney said aboard Air Force One.
The two sides have also struggled to find mutually agreeable ways to slow the growth of health costs, which are projected to nearly double over the coming decade.
Republican Tom Coburn and Senator Joe Lieberman, an independent who usually votes with Democrats, proposed gradually raising the eligibility age for the Medicare program to 67 from 65, and paring benefits for wealthy retirees.
That plan would save more than $600 billion over 10 years, but it was flatly rejected by Democratic leaders. (Additional reporting by Donna Smith, Caren Bohan and Deborah Charles; editing by Mohammad Zargham)