In Florida, Republican Gov. Charlie Crist, who is running for the state’s open Senate seat, said Mr. Brown fits his own mold.

“He sounds like a Charlie Crist Republican, from what I heard,” Mr. Crist said. “Very pragmatic, reasonable, conservative, that understands that the people are in charge and you need to listen to them and serve with a servant’s heart.”

Mr. Crist said Mr. Brown’s message of fiscal responsibility also was a powerful force.

“There is a frustration, if you will, with Washington and the ridiculous spending that’s going on,” he said.