Senate Majority Leader Mitch McConnell hinted Wednesday that he may not support the controversial idea of changing Senate rules to kill Democratic filibusters, and instead warned that Republicans need to be wary of "overreaching" now that they have kept control of Congress.

When Democrats ran the Senate, they changed the rules to allow for simple majority votes for judicial nominees, but not Supreme Court nominees, which can still be filibustered. But despite speculation that Republicans will take this next step, McConnell declined to talk about that option when pressed on Wednesday.

"Well, I won't purport to know what might happen in the context of the Supreme Court," McConnell told reporters. "What we do know is the new president will fill the vacancy …"

He said he "would not expect" Democrats to reveal their strategy for how Democrats might try to defeat the nominee, or how Republicans might respond to that strategy.

And when asked more broadly about how how Republicans and Democrats might cooperate, or not, in the Senate, he struck a conciliatory tone, and warned about "overreaching."

McConnell said "overreaching after an election, generally speaking, is a mistake." When pressed on McConnell's approach to working with Democrats in the new Senate, McConnell said the way the chamber is structured requires "some Democratic participation and cooperation."

The option of ending filibusters on high court nominees has been raised because Republicans have blocked President Obama's nominee, Merrick Garland, for months now. As a result, Democrats are expected to block Donald Trump's nominee once he takes office next year, and some Republicans say another rule change is needed to ensure the nominee can get through.

McConnell congratulated President-elect Trump for a "stunning" victory and said he intended to work with him to respond to voters undeniable message to "change the course of America." He also cited the election results as vindication for his decision to block President Obama's nomination of Garland, which he said prompted a "hail of controversy" over the last several months.

"The people have spoken," he said, adding that President Trump will have the opportunity to name his choice to fill the vacancy on the high court.

This story was corrected to note that McConnell's comment about "overreaching" was not made in response to a direct question about the nuclear option.