The House GOP’s plan to overhaul Medicare isn’t likely to go anywhere in the bipartisan debt limit talks, but that doesn’t mean Medicare reform of some kind won’t be included, Senate Minority Whip Jon Kyl told reporters Monday.

The Arizona Republican said the GOP recognizes that Democrats likely will block House Budget Chairman Paul Ryan’s proposed Medicare overhaul, but Republicans will push for Medicare reforms nonetheless.

Just because the Wisconsin Republican’s proposal to turn Medicare into a voucher for private insurance isn’t likely to get Democratic support, that “doesn’t mean that we shouldn’t try to tackle it,” Kyl said.

Kyl, who represents Senate Republicans in bipartisan debt talks with Vice President Joseph Biden, predicted that in the end, there will be some Medicare reform as part of any overall deal on raising the debt limit. He said that was because it will be hard for Democrats to justify not including it at all.

“It probably won’t satisfy Republicans as much as we think is necessary,” Kyl said.

His comments came after House Republicans struggled last week to both signal a desire to reach a compromise with Democrats and still stand by Ryan’s controversial Medicare blueprint.

Kyl’s assertions drew a rebuke from Jon Summers, spokesman for Senate Majority Leader Harry Reid (D-Nev.).

“So his message to the public is that Republicans will still fight to cut funding for Medicare while continuing to give taxpayer handouts to Big Oil?  Got it,” Summers quipped.

Other Democratic aides said Republicans are starting to realize the political jeopardy that the House budget put them in after some got beaten up on the issue at home during recess.

“There is a strong political reality that seniors and folks across the country don’t like Ryan’s Medicare voucher plan,” one senior Democratic aide said.

With negotiators set to convene again today at Blair House, Republicans made it clear in the first meeting Thursday that they would not accept anything smacking of a tax increase, while Democrats aren’t about to back anything like the vouchers-for-Medicare plan passed by the House.

Both issues seem likely to be resolved by voters in the 2012 elections — leaving it to the negotiators to carve out a smaller deal that includes some upfront spending cuts and spending or deficit caps. Staff talks over the weekend focused on small-ball spending cuts, sources said.

Meanwhile, Senate Democratic Conference Vice Chairman Charles Schumer (N.Y.) tried to amp up the pressure on Speaker John Boehner (R-Ohio) to take a potentially catastrophic default on the federal debt off the table.

Schumer warned that the market could be spooked well in advance of the Aug. 2 deadline set by Treasury Secretary Timothy Geithner.

“If nothing is happening, you know, by July 15th or so, I’d say the markets are going to get really, really worried,” Schumer said.

Michael Steel, spokesman for Boehner, was unfazed.

“The American people flatly reject Sen. Schumer’s call for a blank check for the Democrats who run Washington to keep their spending spree going,” Steel said. “There’s no way an increase in the debt limit will pass without real spending cuts and reforms.”

Boehner was set to propose Monday night that spending cuts exceed the size of debt ceiling increase. Considering it will take a roughly $2 trillion increase in the debt ceiling to get through the next election, Boehner’s position is likely to increase the pressure for major budget cuts.

Kyl said any deal will likely require immediate cuts as well as agreements on spending levels for the next several years at least. And he said Republicans have no interest in running out the clock on the debt limit. “I’m happy to do it as soon as we can do it,” he said.

With bipartisan talks limping along, Senate Democrats continued to negotiate among themselves.

Senate Budget Chairman Kent Conrad (D-N.D.) had hoped to hold a budget markup this week, but that timetable is now in doubt. He said Monday that the chances of holding a markup this week are low as he continues to talk to his colleagues and adjust his proposal after the Congressional Budget Office revised its baseline last week. Conrad also said that the White House’s decision to hold budget summits with Democrats on Wednesday and Republicans on Thursday could affect the markup.

Ranking member Jeff Sessions (R-Ala.) said he was concerned that the White House had scheduled a summit on the budget for this week, while Democrats still haven’t let the GOP see their proposal.

Conrad said that he is still pushing for a roughly $4 trillion cut in the deficit over the next decade and that he won’t sign on to a long-term debt limit increase without a credible long-term plan to deal with the debt. He said Congress may need to enact a short-term increase, perhaps until the end of the year, to buy time to negotiate a broad plan. “I think there may have to be in order to have a credible plan completed,” he said.

Conrad’s plan presents Reid with an extraordinarily tricky job of managing his shrunken Conference. That’s because if Conrad’s budget ever gets to the floor, it will be governed by Senate budget rules allowing unlimited amendments subject to a simple majority vote.

Getting 51 votes for the budget is likely to be an enormously challenging task. Three Senators in the 53-member Democratic caucus have already signed on to tougher spending caps than Conrad will propose, and liberals remain worried that Conrad’s budget starts off too far to the right as they enter negotiations with Republicans.

Reid last week cautioned his flock against signing on to any budget blueprint, including Conrad’s, until they had a better sense of the endgame negotiations with the GOP.

As Democrats dicker over their blueprint, conservative Senate Republicans appear set to take advantage of a quirk in Senate rules that allows anyone to propose a budget resolution and get a vote on a motion to proceed.

Sen. Pat Toomey (R-Pa.) will unveil his budget blueprint today, which he said would balance the budget in nine years — a far more aggressive target than even the budget passed by the House.

Toomey will be joined by fellow conservative Republican Sens. Jim DeMint (S.C.), Marco Rubio (Fla.) and Ron Johnson (Wis.).

Reid has promised a vote on the House budget blueprint as well, but he has not said when that will occur. That will also almost certainly be in the form of a vote on a motion to proceed, which Democrats can easily defeat, rather than on the budget itself. That’s because once a budget resolution actually gets to the floor for debate, Budget Act rules apply, including unlimited amendments.

Senate Minority Leader Mitch McConnell (R-Ky.) has promised to respond in kind with a vote on President Barack Obama’s original budget proposal, which would likely get even fewer votes, given that Obama has since acknowledged his plan fails to put the nation on a sustainable path.

Editor’s note:

The online version of this article has been updated with comments from Senate Budget Chairman Kent Conrad (D-N.D.).