The congressman’s efforts to impeach the president, just six months into his term, have virtually no chance of succeeding given the strong majority Republicans hold in the House, where impeachment proceedings must begin.

“Impeachment is not purely a legal issue,” said Elaine Kamarck, a former Clinton administration official who is now a senior fellow at the Brookings Institution and author of “Why Presidents Fail.” “It’s a legal and political issue, and the politics here haven’t gotten to the point of impeachment even though it looks obvious there are several legal cases that can be built.”

Representative Jim Sensenbrenner, Republican of Wisconsin and a member of the House Judiciary Committee, condemned Mr. Sherman’s efforts.

“Frustrated opponents of the president are grasping at straws and factitious rumors to advance their own political agenda rather than the interests of the country,” Mr. Sensenbrenner said in an emailed statement. “There is no proof of wrongdoing on the part of the president, which means discussions of impeachment are not only premature, but imprudent and counterproductive.”

While a handful of Democratic lawmakers, including Representative Al Green of Texas, have been pushing for the president’s removal in recent weeks, others in the party have tried to play down calls for impeachment to keep the spotlight on policy issues such as health care.