WASHINGTON — From the House that Newt Gingrich once ran through the Washington establishment to state capitals across the nation, some Republicans are going public with their concerns that Mr. Gingrich would be a weak general election candidate and a drag on the party’s fortunes if he won the presidential nomination.

“Since we don’t know how he got here, I don’t know how he can be stopped,” said Ed Rogers, a longtime Washington lobbyist and party strategist who worked for the first President George Bush.

Mr. Rogers, who has not endorsed anyone, is like many in the party who esteem Mr. Gingrich for his achievement in leading Republicans to the control of Congress in 1994, after 40 years in the House minority, but who recoil from the prospect of him at the top of the ticket given the controversy, scandal and electoral defeats that defined his four years as speaker.

Late Saturday, former Senator Bob Dole, the 1996 Republican nominee, endorsed Mitt Romney, whose campaign is now anticipating a long and hard-fought nominating battle against Mr. Gingrich. Last week, Mr. Romney won the endorsement of Gov. Nikki R. Haley of South Carolina, which holds the first Southern primary, on Jan. 21.