That vote could come as early as Friday or over the weekend.
Senate Democrats made clear they will not agree to reopening the government on a piecemeal basis. "You can't fall for that legislative blackmail or it will get worse and worse and worse," said Sen. Chuck Schumer of New York.
Speaking at a construction company in Washington's Maryland suburbs Thursday, Obama cast Boehner as a captive of a tight group of conservative Republicans who want to extract concessions in exchange for passing a short-term spending bill that would restart the partially shuttered government.
"The only thing preventing people from going back to work and basic research starting back up and farmers and small business owners getting their loans, the only thing that is preventing all that from happening right now, today, in the next five minutes is that Speaker John Boehner won't even let the bill get a yes or no vote because he doesn't want to anger the extremists in his party," Obama said.
Senate Majority Leader Harry Reid, D-Nev., was even more pointed in singling Boehner out.
"We can't perform the most basic functions of government because he doesn't have the courage to stand up to that small band of anarchists," he said.
Moderate Republicans have said they think they could provide enough votes to join with minority Democrats and push a bill through the House reopening the government with no restrictions on the health care law. But under pressure from House GOP leaders, they failed to join Democratic efforts on Wednesday aimed at forcing the chamber to consider such legislation.
Rep. Tom Cole, R-Okla., who is close to Boehner, said he doesn't think the speaker is ready to push any measure that would fail to win the backing of most of his 232 House Republicans. But some Democratic votes eventually will be needed in the 435-seat chamber, Cole said, because some hard-core conservative Republicans are unlikely to vote to end the shutdown or raise the debt ceiling without major concessions from Obama.