The president said in remarks (after commenting on a newly-sealed free trade pact with South Korea) that he wasn't happy that.
But Mr. Obama told reporters, "With so much at stake, today's votes cannot be the end of the discussion."
"We need to get this resolved and I'm confident we can do it," he said. He said he'd work through the weekend and into next week to find a compromise.
President Obama said lawmakers must give the American people "the peace of mind that their taxes will not go up" come the new year. He said that will require compromise by both sides.
The Senate Saturday voted on two bills that would have permitted tax cuts to remain in effect at most incomes. Democrats knew going in that both would fail, but wanted to use the votes to cast Republicans as protectors of millionaires.
President Obama repeated his position that it didn't make sense to extend tax cuts for the wealthy - individuals with incomes over $200,000 and couples over $250,000.
He didn't say what kind of deal he'd embrace, but a temporary extension of all the tax cuts is emerging as the likely compromise.
President Obama also emphasized the importance of extending unemployment benefits, which just expired. That's expected to be part of any agreement. He said it was "simply wrong" for people to lose jobless benefits in the holiday season.