House Republicans have submitted a revised short-term proposal to raise the federal debt ceiling and reopen the government, offering President Obama another option Friday as he hosted Senate Republicans at the White House in an effort to build on the first signs of bipartisan progress on the issues.

While Senate Republicans were meeting with Obama over how to deal with next week’s debt-ceiling deadline and the 11-day-old federal government shutdown, House Republicans were waiting to hear back from the administration about the updated proposal they submitted late Thursday.

Their original proposal only addressed the debt ceiling, but the new plan addresses both the shutdown and debt ceiling.

Under the new proposal, the House would vote as soon as Friday evening on a plan to raise the debt limit through Nov. 20 — the week before Thanksgiving — to create space for talks over broader budget issues. Republicans have also offered to reopen the government as soon as next week in a bill that would replace some of the deep budget cuts known as the sequester with cuts to entitlement programs, including Medicare, according to people familiar with the proposal who spoke on condition of anonymity. Replacing the sequester is a top Democratic priority, while cutting entitlement programs is a leading GOP priority.

But details of the proposals were murky, and there was no clear quid pro quo linking one priority to the other.