"There are enough Republican and Democratic votes in the House of Representatives to end this shutdown immediately," Obama told employees of the Federal Emergency Management Agency, during an unannounced visit.
A White House official said Obama wanted to "thank federal employees for their hard work" despite the government shutdown.
With many workers furloughed and others working without pay, FEMA has made efforts to help residents preparing for Tropical Storm Karen as well as those facing severe weather which has battered parts of the Midwest.
With little sign of a breakthrough in the week-long government shutdown, Obama also used the visit to hammer Republican lawmakers, urging them to pass a clean continuing resolution.
"Now you’re being put back on furlough” because of the government shutdown, Obama told FEMA workers.
"That’s no way of doing business," he added.
Obama said Democrats had already compromised on fiscal issues.
"We are willing to pass a bill that reflects the Republican priorities in terms of funding levels. That’s a pretty significant compromise," he said.
The nation also risks default and a credit downgrade if lawmakers do not raise the borrowing limit by Oct. 17.
Boehner on Sunday said there were not enough votes for a clean funding measure to pass the House.
GOP lawmakers say they want the president to negotiate with them over Obamacare and further spending cuts and entitlement reforms.
House Republicans have passed funding bills that include measures delaying or defunding Obamacare. But those bills were rejected by the Democratic-controlled Senate.
"Yesterday, contrary to press reports, Speaker Boehner said that he didn’t have the votes to pass a clean Continuing Resolution to reopen the government," said a White House official ahead of Obama’s remarks.
"The administration and Democrats in Congress are asking the Speaker to prove that a majority in the House would not vote for the Senate-passed bill to reopen the government by holding an up-or-down vote on the clean Continuing Resolution to end this impasse that is impacting vital services provided by agencies across government, including FEMA."
Republicans have passed legislation to reopen specific agencies and restore certain government services, but Senate Majority Leader Harry Reid, D-Nev., and the White House have rejected them, insisting on a lone comprehensive funding bill.
Boehner spokesman Brendan Buck urged Senate Democrats to pass and for Obama to sign a House bill that restores funding for FEMA.
“If the president and Washington Democrats want FEMA up and running, they have the ability to make it happen today,” said Buck in a statement.
This story was published at 12:30 p.m. and has been updated.