(CNN) House Speaker Nancy Pelosi and Senate Democratic leader Chuck Schumer both made clear Tuesday that censuring President Donald Trump, as some prominent Democrats have suggested, is not on the table.

"We have impeached the President," Pelosi, a California Democrat, said to a group of reporters in advance of the President's State of the Union address. "Our house has spoken."

As she started to make the case that Republican senators -- led by Senate Majority Leader Mitch McConnell of Kentucky -- wouldn't go for the option anyway, Schumer finished the thought.

"Mitch McConnell -- we cannot bring it up in the Senate trial," the New York Democrat said. "He has the ability to bring it up afterwards. He won't. But for most of us, and just about all of us, he should be convicted and we don't want a halfway measure."

Schumer continued, "I think the reason McConnell doesn't want to bring it on the floor is our Republican colleagues -- so many of them -- are so afraid of even saying he was wrong that they don't want to have a vote on it."

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