As for the deeper problem of the federal debt ceiling, the administration has warned that unless the limit is raised, the government will deplete its ability to borrow money by next Thursday, an event officials have warned could trigger a default that could wound the world economy as well as America's .
Obama has steadfastly insisted that Congress reopen the government and extend the debt limit without conditions. His acceptance of the GOP proposal could mean a brief resolution to the fight over the debt limit and a continuation of the shutdown while negotiations proceed.
Republicans have been demanding cuts in government programs, including Obama's 2010 health care law, and a bigger effort to cut long-term federal deficits as their price for reopening government and extending the debt limit.
Obama has repeatedly noted recent improvement in the deficit figures. After four years of trillion-dollar deficits, the 2013 shortfall is expected to register below $700 billion.
Some conservatives still expressed reservations with the Boehner plan. "I'm not very enthusiastic about that," Rep. Steve King, R-Iowa, said.
Under Boehner's offer, the House would also appoint negotiators to bargain with the Democratic-led Senate over a budget compromise. Those talks have been on hold for months, and the two chambers have deep differences over taxes and cuts in benefit programs.
Earlier Thursday, Treasury Secretary Jacob Lew warned the Senate Finance Committee that failure to renew the government's ability to borrow money "could be deeply damaging" to financial markets and threaten Americans' jobs and savings. It would also leave the government unsure of when it could make payments ranging from food aid to Medicare reimbursements to doctors, he said.
"The United States should not be put in a position of making such perilous choices for our economy and our citizens," the secretary said. "There is no way of knowing the irrevocable damage such an approach would have on our economy and financial markets."