(CNN) Senate Republicans on Monday both praised and expressed skepticism about the decision by House Democratic leaders to vote on an impeachment resolution, saying they hope it will open up the process and provide fairness to President Donald Trump.

At the same time, some GOP senators strongly doubted that the House Democrats are prepared to do anything short of impeaching him.

"It's about time," declared Sen. David Perdue, a Republican from Georgia and close ally of Trump's who said he wants to study the resolution to see if "it's really going to provide due process" to the inquiry that's been underway for several weeks.

Republicans also warned that so much damaging information about Trump has "selectively leaked" out of the closed-door depositions in the House impeachment probe that a "vote now is a bit like un-ringing a bell," according to Sen. Lindsey Graham, a Republican from South Carolina.

GOP senators, who are would-be jurors in an impeachment trial, took credit for forcing Speaker Nancy Pelosi to vote on the resolution after Senate Majority Leader Mitch McConnell and Graham, who chairs the Judiciary Committee, unveiled a resolution last week criticizing how House Democrats have handled the inquiry, pressing them to hold a floor vote to formally initiate it and to allow Trump to call witnesses on his behalf and Republicans to issue subpoenas.

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