“Support for Rick Perry has diminished dramatically here,” said Charles Moncrief, a Fort Worth oil man who has sat on Mr. Perry’s campaign-finance committee and says he has “known Rick forever.” Mr. Moncrief and his wife, Kit, gave Mr. Perry $5,000 in August, but Mr. Moncrief said he is now giving to Mr. Romney and isn’t sure if he’ll give any more to Mr. Perry.

“Perry’s done this to himself,” he said. “He’s really hurt himself.”