WASHINGTON — A bipartisan group of senators is polishing a plan that would reopen the government and prevent an unprecedented default on the country’s bills.

Meanwhile, talks between the White House and House Republicans for a way out of the financial mess have stalled.

Senators planned to vote Saturday on a Democratic measure to lift the government’s borrowing cap through the end of next year. Republicans were poised to reject it.

Senate leaders were keeping close watch on the work by the bipartisan group. An emerging proposal by Sen. Susan Collins, R-Maine, and others would pair a six-month plan to keep the government open with an increase in the government’s borrowing limit through January.

House Republicans received an update from Speaker John Boehner of Ohio before beginning their weekend session: “There is no deal or negotiations going on,” he told colleagues, according to Rep. Richard Hudson of North Carolina.

The shutdown limped into its 12th day and an ominous deadline neared: The Obama administration says the government will bump up against its borrowing limit Thursday, raising the specter of an unprecedented default.

President Obama met Senate Republicans on Friday and heard a pitch from Collins on raising the debt limit until the end of January, reopening the government, and cutting the health care law at its periphery.

The plan also would strengthen income verification for people receiving subsidies through the health care law and set up a broader set of budget talks.

The Collins proposal would delay for two years a medical-device tax that helps finance the health care law, and it would subject millions of individuals eligible for subsidies to buy health insurance under the program to stronger income verification.