"There is this almost created sense of this Mighty Mouse candidacy, 'Here I come to save the day,"' Huckabee told reporters after giving a speech at a financial services company. "In the end, voters are not necessarily looking for someone to come in and save the day."
Huckabee said voters are looking for consistency and authenticity — a veiled jab at rival Republicans who have changed positions throughout their careers.
Thompson, the "Law & Order" actor, is edging closer to a full-blown candidacy that could shake up the GOP field. He leads Huckabee and others in the crowded second tier of the Republican field in some polls.
The former Arkansas governor said history teaches that great expectations often fizzle.
"For most (such) situations, there is certainly this buildup anticipation of people until they actually enter the race. Then it's 'OK, let's go find someone else to go get excited about,"' Huckabee said.
He cited the "incredible anticipation" four years ago as retired four-star Gen. Wesley Clark edged closer to his presidential announcement.
"He got in, and things never really got any better. The best it was, was the day before he made the announcement," Huckabee said.
He declined to predict whether Thompson would flame out if he gets into the 2008 race.
Huckabee was campaigning for a second day in the first-primary state before a nationally televised debate Tuesday night in Manchester. During the last round of debates, Huckabee dispatched a joke about former Democratic Sen. John Edwards' hair that earned repeats.
"We've had a Congress that's spent money like John Edwards at a beauty shop," he said, mocking Edwards' $400 haircuts.
Huckabee said he doesn't know who will be his punch line Tuesday.
"I don't know about another John Edwards joke. I hope I get an opportunity to be myself," he said. "I'm always working on new material because my wife says my old material stinks."