The Knicks play in San Antonio on Thursday, in Houston on Friday and in Dallas on Sunday, in what is known as the "Texas Triangle" gauntlet.
The Knicks will be without Raymond Felton for at least three more games.
"They haven't practiced, so we got three games in four days I think it is," Woodson said. "It's going to be impossible for them to play."
Felton worked on the side at practice Tuesday as he nurses a strained right groin, while Prigioni did not work due to the hairline fracture of his right big toe. Felton last played on Dec. 10, while Prigioni has been out since Dec. 16. Prigioni was scheduled to miss at least two weeks.
"Raymond and Pablo are still a little bit away," Woodson said. "They're not on the floor yet in terms of pounding and running, so we have to basically wait."
With those two out, the Knicks have been forced to extend players who normally wouldn't be receiving quality minutes. Third-string point guard Beno Udrih has been starting, and the team has been forced to use Toure' Murry for extended minutes. The Knicks cut Chris Smith on Tuesday and replaced him with big man Jeremy Tyler.
"Yeah, we are short-handed from a point guard standpoint, but we got to pray that Raymond and Pablo will be back in a uniform soon because we need those two guys," Woodson said.
Felton has been disappointing this season, averaging just 10.5 points and 5.1 assists per game, and he has missed 13 of the team's first 30 games. Prigioni is averaging 3.9 points and 3.2 assists per game.
Anthony practices: Forward Carmelo Anthony (ankle) did some work on the floor with some contact Tuesday, according to Woodson. It's still unknown whether Anthony will be able to play against San Antonio.
"We'll see how he feels tomorrow after the workout today," Woodson said.
Anthony has missed the past three games with a sprained left ankle, but is hoping to return Thursday against the Spurs. He said Monday he had "swelling" and "tenderness" in his ankle. The Knicks are 0-3 without him, and have been outscored by 67 points since he left in the third quarter against the Orlando Magic on Dec. 23.
"It was definitely disappointing, sitting back watching it. I definitely hate sitting out watching the games," Anthony said Monday. "I’m trying to do what I have to do to get back and do what’s best for everybody."