DES MOINES — Republican leaders are growing alarmed by the ferocious ways the party’s mainstream candidates for president are attacking one another, and they fear that time is running out for any of them to emerge as a credible alternative to Donald J. Trump or Senator Ted Cruz of Texas.

Leaders of the Republican establishment, made up of elected officials, lobbyists and donors, are also sending a message to the mainstream candidates, such as former Gov. Jeb Bush of Florida, that they should withdraw from the race if they do not show strength soon.

The members of the party establishment are growing impatient as they watch Mr. Trump and Mr. Cruz dominate the field heading into the Iowa caucuses on Monday and the New Hampshire primary eight days later.

Party leaders had hoped that one of their preferred candidates, such as Senator Marco Rubio of Florida, would be rising above the others by now and becoming a contender to rally around.