The Swiss face a U.S. team led by Andy Roddick and James Blake when first-round play in the best-of-five series begins Friday.
Federer, a 13-time Grand Slam winner now ranked No. 2, is out with a bad back.
"We know for Roger it wasn't an easy decision to make, but I think it's very important for his career that he make this decision,'' said Stanislas Wawrinka, now his country's top singles player at No. 18.
Swiss captain Severin Luthi said it would have been tough beating the Americans even with Federer.
"I think after Roger pulled out, for sure we're not the favorites any more,'' Luthi said. "We're the outsiders, but we're comfortable in this situation. For sure we didn't come here to lose. We're going to do the maximum and try to win this tie.''
After Wawrinka it's not clear who will be Switzerland's No. 2 player.
"It's always the same with our team,'' Luthi said. "We're always ready to change.''
The matches will be played on a hard court at the Birmingham-Jefferson Convention Complex. The winner advances to the World Group quarterfinals in July; the losers are off until September.
Roddick acknowledges that Federer's absence "took a little bit out of the match.''
"It's a weird dynamic because obviously it increases our chances of winning having him not be here,'' he said at a news conference.
In October, Federer committed to the first round of the Davis Cup for the first time since 2004. But in January he backtracked because of his back, which has been ailing since last year. His teammates had his support. Some at home, however, were perplexed.
"For sure people were disappointed, and a few of them maybe couldn't understand it,'' Wawrinka said.
This is the first time the Davis Cup has been played in Alabama and early ticket sales were strong based partly on the Federer-Roddick matchup. Organizers said Federer's absence hadn't hurt the event.
"We have not had one single phone call to our office requesting a refund,'' said Gene Hallman, executive director of the Alabama Sports Foundation.
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AP Sports Writer John Zenor contributed to this report.
