However, conservatives wanted more.
Republican, Rep. Cynthia Lummis of Wyoming told CNN that she was undecided but wanted to see deeper budget cuts on the measure.
"I came here to cut spending and to reduce the size of the federal government, so when those opportunities arise I want to take advantage of them," Lummis said.
Obama said Friday that the GOP strategy amounts to threatening to "burn the house down simply because you haven't gotten 100% of your way."
"That's not how our democracy is supposed to work," he said, repeating his past insistence that he will not negotiate under threat of a U.S. default because Congress failed to increase the debt ceiling.
White House spokesman Jay Carney told reporters on Thursday a one-year delay in implementing Obamacare's individual mandate for people to obtain health insurance would undermine a key provision of the program that prohibits the denial of coverage due to pre-existing conditions.
"The fact is you have to make the system work," Carney said, adding people with pre-existing conditions won't be denied insurance under Obamacare "because of the expansion of the number of people who will be covered and participate in these marketplaces provided by the Affordable Care Act through the individual mandate."
CNN Chief National Correspondent John King said Thursday that focusing on the debt ceiling was where House Republicans "wanted to wage this fight all along."
"They didn't want to get bogged down in the government shutdown fight," King said, "but a conservative revolt within the House Republican ranks forced them to get there."