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.