Connecticut Congressman Jim Himes, a Democratic member of the House Intelligence Committee, said Democratic lawmakers have enough support to authorize an impeachment inquiry of President Trump if such a resolution were to be brought up for a vote on the House floor, as some Republicans have demanded.

"If Speaker Pelosi did in fact move forward with a floor vote on actually proceeding with an investigation — which as you point out is not required here — there's no question in my mind that she would have the votes," Himes said on "Face the Nation" Sunday.

Late last month, Speaker Nancy Pelosi announced a formal impeachment inquiry of Mr. Trump after revelations first emerged that he and his administration pressured the Ukrainian government to open investigations into his political rivals, including former Vice President Joe Biden and his son, Hunter.

Republican leaders in the House, however, have portrayed the announcement as a politically motivated ploy to hurt Mr. Trump's reelection prospects, with Minority Leader Kevin McCarthy asking Pelosi on Thursday whether she plans to hold a full vote to authorize the inquiry Democrats have already launched.

The White House is also expected to send Congress a letter this week saying it will not recognize the impeachment inquiry until there is a floor vote to authorize it.

In response to McCarthy's letter last week, Pelosi said there's no requirement under the Constitution or House rules to hold a vote on the House floor before conducting an impeachment inquiry.

Asked if a resolution voted by the full House to approve an inquiry could help Democrats counter Republican efforts to discredit the investigation, Himes suggested it would be counterproductive to focus on trying to appease the concerns of their colleagues on the other side of the aisle.

"Well, you know, if you try to spend your time killing Republican talking points, you'll do nothing else," he said.

He cited another Republican talking point to defend his position.

"I mean, I heard it from Senator Blunt just now: 'You know leaders ask other leaders for favors,'" Himes said. "Yeah, that may be true. I'm sure presidents have in the past asked other leaders for favors. Traditionally those favors have not been research my political opponents."

Paula Reid and Weijia Jiang contributed reporting.