Cognizant of Bush's popularity, she stressed that she backed the administration about three-fourths of the time in key congressional votes.
But Terrell, 48, the state's elections commissioner, countered that the president would be best served by adding another Republican to the Senate.
In a series of televised debates and in dueling TV advertisements, Landrieu and Terrell traded sharp attacks.
Landrieu charged that Terrell had been a lobbyist for a foreign drug company.
Terrell attacked the senator as a liberal akin to Sen. Hillary Rodham Clinton (D-N.Y.) in a radio ad that featured an impersonation of ex-President Clinton. She also accused Landrieu of abandoning the Roman Catholic faith on the question of abortion.
Terrell, also a Catholic, backs a constitutional ban on abortion. Landrieu supports abortion rights, with some exceptions.
Their public exchanges grew so strained that Landrieu told Terrell after one debate, "This is your last campaign."
The challenger afterward said she interpreted that remark as a threat.
Before the polls closed, both parties mounted a frenzied push to turn out their supporters. Mailboxes were flooded with brochures. Campaign workers leafleted doorsteps and knocked on doors. Others stood on street corners and waved signs to remind people to vote.
Then there were the automated "robo-calls."
Republican gun owners -- some of whom were outdoors on the first day of hunting season -- were targeted with a tape-recorded telephone message from Vice President Dick Cheney. Military veterans leaning toward the GOP heard from former Senate Majority Leader Bob Dole, a World War II veteran.
On the Democratic side, former President Clinton taped a telephone call directed at black voters. Many also received phone messages from Sen. John B. Breaux, a popular centrist Democrat, and Rep. William J. Jefferson, who is influential among black voters in New Orleans.
Several black members of Congress also have traveled to the state in recent days to help Landrieu, including Rep. Maxine Waters (D-Los Angeles).
Anderson reported from Washington, Hart from New Orleans.