Updated 7:48 p.m.

House Republicans brought up billions of dollars in potential cuts to Medicare on Monday, in the latest round of debt-limit talks, but the White House and congressional Democrats rejected the idea in part because it did not include any increases in tax revenue.

According to a Democratic aide with knowledge of Monday’s meeting, President Obama asked Republicans after the group’s Sunday-night meeting to return on Monday with specific deficit-reduction ideas put on paper.

House Majority Leader Eric Cantor (R-Va.) returned Monday afternoon and described a plan that included $250 billion in cuts to Medicare over the next decade, the aide said. Among the deficit savings were $53 billion in cuts to the Medigap supplemental insurance program and $38 billion in means-testing.

Cantor spokeswoman Laena Fallon confirmed that her boss brought up the cuts and said they “were identified in the Biden talks and discussed by the vice president and the bipartisan participants in the talks as an area of potential savings.”

“It wasn’t a new proposal by any stretch of the imagination,” Fallon said.

Cantor’s office maintains that the group led by Vice President Biden had identified at least $2 trillion in deficit savings before House Republicans left the talks late last month. The White House says that the number is closer to $1.8 trillion.

House Democrats pushed back Monday against the inclusion of any entitlement cuts in a final deal.

“We continue to oppose benefit cuts in Social Security and Medicare,” House Minority Leader Nancy Pelosi (D-Calif.) said in a statement. “These pillars of economic and health security should not be used as a piggybank to subsidize tax cuts for the wealthy.”

Also discussed at Monday’s 90-minute meeting were various “firewall” proposals to protect certain programs. According to a Republican aide with knowledge of the talks, House Speaker John Boehner (R-Ohio) told participants that any firewall would be met with opposition on both sides.

The Huffington Post reported Monday that the White House floated the idea of increasing the Medicare eligibility age to 67 from 65 if Republicans would agree to tax increases in a final debt-limit deal.

The group’s next meeting is at 3:45 p.m. Tuesday at the White House. Participants were told Monday to speak with their respective caucuses and try to figure out a way forward.

(This post has been updated to revise the headline and add mention of the Huffington Post’s report.)