Andy Roddick had to withdraw from the Delray Beach tournament Monday because of flulike symptoms. Sam Querrey's shoulder is sore. Mardy Fish isn't available because of a thyroid problem.
The Americans will play outdoors on clay at Santiago, Chile, in a first-round match March 4-6.
"These guys are tough, and we're not excuse makers," Courier said on a conference call Tuesday. "We'll be ready to play and ready to battle when we get down there."
Courier expects the eighth-ranked Roddick to recover in plenty of time. The 22nd-ranked Querrey wasn't on the four-man roster the U.S. had to provide to the International Tennis Federation on Tuesday. But he is scheduled to travel to Chile, and Courier can change as many as two players before the final lineup is submitted March 3.
Courier isn't sure Fish is ready for a five-set match because of the thyroid problem that has sapped his strength. But he wants the 16th-ranked veteran back on his roster if the Americans advance.
Courier spent last week at the Memphis tournament, where he could be around all four of his singles players.
"It's a very delicate environment to be sitting on a court with a player and having a chance to influence them, and you have to be very sensitive to how they normally operate, which is what I'm trying to find out through their coaches and what their tendencies are," Courier said.
As a player, he was generally comfortable talking to his Davis Cup captain during matches.
"Some players like Pete (Sampras) didn't want to talk," Courier said. "They just wanted to play. So you just have to know your audience, like anything in life."
Chile submitted a roster of Paul Capdeville, Jorge Aguilar, Nicolas Massu and Guillermo Rivera, none of whom are ranked in the top 100 in the world.
Other teams will also be missing top players. France will be without 12th-ranked Gael Monfils and No. 17 Jo-Wilfried Tsonga because of injuries against Austria. The deep French can still use No. 27 Michael Llodra, No. 28 Richard Gasquet and No. 33 Gilles Simon.
Davydenko, who reached the final in the season opener in Doha, Qatar, in January, was eliminated in the first round of the Australian Open and in the next two tournaments. He asked captain Shamil Tarpischev not to call on him.