"He's strong, and he doesn't waver," said Jaren Olsen, 18, a freshman at Brigham Young, the nation's largest religiously affiliated private university, who is from Albany. "I like that he is for the family, that marriage should only be between a man and woman. And the war, we need to finish what we started."

Another student at Brigham Young, Danielle Pulsipher, a junior, offered blanket approval of the president. Asked to name which of his actions as president she liked most, she was hard-pressed to answer.

"I'm not sure of anything he's done, but I like that he's religious — that's really important," Ms. Pulsipher said.

Image Kelly Patterson of the Center for the Study of Elections and Democracy. Credit... George Frey for The New York Times

Not that Mr. Bush is immune from national political trends even among the most faithful.

A poll released in May by SurveyUSA, conducted in Utah for KSL-TV, found that 51 percent of respondents approved of the job Mr. Bush was doing, with 46 percent disapproving. The margin of error was plus or minus four percentage points. The firm, through its other polling, found that the only other state above 50 percent was Idaho, at 52; in Wyoming, it was 50 percent. Mr. Bush's approval rating has dropped as low as 23 percent in Rhode Island and New York.

In Utah, Mr. Bush took 72 percent of the presidential vote in 2004. His support has dropped since then, according to polls, because many conservatives are upset over immigration and, to a lesser extent, the expansion of the federal government.

"When you get down to almost 50 percent in Utah, that's the canary-in-the-mine-shaft of all warnings for Republicans," said Kelly Patterson, director of the Center for the Study of Elections and Democracy at Brigham Young. The walls of Mr. Patterson's office bear a headline from the last time a Democrat won Utah in a presidential race — it was Lyndon B. Johnson, in 1964.