Senate Democrats and Senate Republicans last week put forward alternatives that would have avoided the cuts, but each side voted down the others' proposals. The House Democrats proposed an alternative but the House Republicans did not let them vote on it.
House Republicans twice passed alternatives last year.
Obama has phoned lawmakers but it isn't clear to what end; the White House refused Sunday to release the names of lawmakers Obama phoned. Boehner and McConnell said they had a productive meeting with Obama on Friday, but it didn't yield a deal.
"Well, no one can think that that's been a success for the president," said Mitt Romney, Obama's unsuccessful rival in November's election. "He didn't think the sequester would happen. It is happening."
Obama and the Republicans have been fighting over federal spending since the opposition party regained control of the House of Representatives in the 2010 midterm elections. The budget cuts were designed in 2011 to be so ruthless that both sides would be forced to find a better deal, but they haven't despite two years to find a compromise.
The $85 billion in cuts apply to the remainder of the 2013 fiscal year, which ends Sept. 30. But without a deal they will continue slashing government spending by about $1 trillion more over a 10-year period.
McConnell spoke to CNN's "State of the Union." Boehner was interviewed on NBC's "Meet the Press." Sperling appeared on ABC's "This Week," NBC and CNN. Ayotte appeared on ABC. Graham spoke with CBS' "Face the Nation." Romney was a guest on "Fox News Sunday."