While Jordan and Meadows have gathered a group of nine other GOP lawmakers to co-sponsor their motion, not all House Republicans support Rosenstein's impeachment.
House Speaker Paul Ryan said during a news conference Thursday he does not back impeaching Rosenstein.
"I do't think that this rises to the level of high crimes and misdemeanors," Ryan said.
Rep. Trey Gowdy, a critic of Rosenstein who has been deeply involved in the House investigations into the surveillance warrants on Page, suggested Wednesday night that impeachment was not the best option to pursue.
Gowdy said, "Impeachment is a punishment, not a remedy" shortly before the motion was introduced.
"If you are looking for documents, then you want compliance, and you want whatever moves you toward compliance," he added.
The defection of Gowdy, in particular, from his Republican colleagues is noteworthy. He is the chairman of the House Oversight Committee, which has in the past joined other House committees in criticizing Rosenstein and calling for a second special counsel to investigate Page's FISA warrant.
He also was the only member of the House Intelligence Committee to read the primary documents from the secret surveillance court that supplied the source material for an incendiary memo pushed by Trump ally Rep. Devin Nunes, R-Calif., in February.
After that memo was made public, Gowdy reaffirmed that he was "100 percent confident" in Mueller.
Sen. Jeff Flake, R-Ariz., said in a tweet Wednesday night that he "does not agree" with the articles of impeachment.