WASHINGTON — Senate Minority Leader Mitch McConnell says he and the White House have agreed on preventing tax hikes that the “fiscal cliff” will trigger after midnight. And he says they are very close to an overall deal that would also prevent budget-wide spending cuts.

The Kentucky Republican did not provide any details. But he said on the Senate floor that lawmakers should pass legislation averting tax increases that would otherwise take effect at the start of New Year’s Day.

McConnell spoke after President Barack Obama said in televised remarks from the White House that a deal was in sight.