The Democratic measure failed 51-49. Democratic Sens. Kay Hagan of North Carolina, Mary Landrieu of Louisiana, Mark Pryor of Arkansas and Senate Majority Leader Harry Reid of Nevada voted with Republicans against the bill.

Both sides seemed publicly cemented in their positions Thursday.

At the White House, Press Secretary Jay Carney mocked the Republican proposal, asserting that “no amount of flexibility changes the fact that these severe cuts threaten thousands of middle-class jobs and slash vital services for children, seniors, and our troops and military families.”

Obama hopes “that Republicans, whether it’s the short term or the long term, are ready to talk seriously about compromise and making sure that Washington is not inflicting wounds on the economy right when the economy should be growing and creating jobs,” Carney said.

Boehner and McConnell didn’t sound like they were in compromising moods Thursday.

“The president and the Democrat leaders have failed to pass a solution of their own,” Boehner told reporters. “My message at the White House will be the same as what I’m telling you today. It’s time for them to do their job.”

McConnell said he plans to make clear to Obama Friday that “the American people will simply not accept replacing spending cuts agreed to by both parties with tax hikes.”

“No more protecting waste and broken programs at the expense of those who actually need government help,” McConnell said. “The American people were promised more spending control, and Republicans are going to help them see that that promise is fulfilled – and in the smartest way possible.”

Even before Thursday’s votes and Friday’s meeting, congressional Democrats and Republicans were looking ahead, suggesting that the cuts could be restored, or at least reconsidered, in budget fights to come. That’s likely to come over the next three weeks when government funding expires March 27, requiring new budget legislation called a continuing resolution.

“What I would hope is that the Republicans there, both of them, would agree with their Republicans around the country that we should have a balanced approach to get rid of this and look forward to the sequestration, which is the 27th of next month,” Reid said. “It would be so easy to do. There are things that they’ve agreed to in the past on taking – getting rid of some of the tax loopholes and doing things of that nature that we could have a balanced approach.”