WASHINGTON  It’s the week before Election Day. Do you know where your president is?

Probably not, and that is by design. With Senator John McCain lagging behind in the polls and many other Republicans fighting for their political lives, the nation’s top Republican  President Bush  is intentionally lying low this week, and is likely to do so until after Americans cast their ballots to pick his successor.

Mr. Bush, an ardent student of politics, knows what it feels like to be down in the polls, and he is keeping a careful eye on the campaign. Earlier this week, he made a surprise visit to the headquarters of the Republican National Committee to offer thanks to those who have served him for the past eight years, and deliver a little pep talk to lift the spirits of beleaguered McCain supporters.

“He talked about how he was never supposed to win a campaign,” said one person who attended, speaking anonymously because the session was off-the-record. “He talked about how in ’94, 2000, 2004, they always said he had no chance, and he just encouraged us, to say it’s just important to keep doing what we’re doing and keep working hard.”

The message was not entirely surprising. What was striking is that Mr. Bush chose to deliver it in private. Presidential visits to campaign headquarters are routine business in election years; the day before voters cast their ballots in 2000, President Bill Clinton dropped in on Democratic headquarters in Little Rock, Ark. to buck up campaign volunteers, even as he conceded that he had no idea which way the race between Vice President Al Gore and Mr. Bush, then the governor of Texas, would go.