The initial report came from ESPN's NFL Insider Adam Schefter. Schefter stated on Twitter that Romo has been ruled out of the rest of the season, citing a league source.
Fellow ESPN analyst Chris Mortensen reported, also citing sources, that Romo has suffered a herniated disc and surgery is necessary.
Around an hour after Schefter's tweet, Cowboys head coach Jason Garrett held a press conference where he did not confirm those reports and said after undergoing an MRI, Romo's status is day to day.
"We have not made that determination at all at this point," Garrett said. "With any player, the day after the game, you want to see what the injury is and we've done that with Tony and we want to get him involved in treatment as quickly as we can, and we've started that process."
Romo completed 17 of 27 passes for 226 yards with two touchdowns in Dallas' 24-23 win over the Washington Redskins yesterday.
He played much of the game with back pain. Romo was limping noticeably after a couple of plays in the fourth quarter.
"In the fourth quarter, he appeared to be in trouble even more after spinning free from the pocket on a third-down throw to Miles Austin. Romo appeared to kick the back of his leg as he escaped trouble, but he did not miss a snap," according to ESPN.com.
"I took a hit that kind of triggered it a little bit. ... I felt it after that play, the rest of the game," Romo said in a press conference after the game. "You just play through it, just like anything in football."
Romo has dealt with numerous injuries over the years, including a broken rib in 2011. He hurt his ribs again in last year's season-ending loss to the Redskins.
Garrett said Romo is suffering from a hip or back injury.
"He's going to get treatment each day. He's been getting treatment all day today and he'll continue to get it. We'll evaluate on a day to day basis and see what his status is Wednesday and for this coming week," Garrett said.
If Romo is out, quarterback Kyle Orton is expected to play Sunday when the Cowboys host the Eagles. Garrett says, the team will sign another quarterback in the wake of Romo's injury.
"Just because Kyle Orton is the only other quarterback we have on our roster, we don't have a quarterback on our practice roster. We'll probably make that determination in the next couple days," Garrett said.
Action News sports reporter Jeff Skversky says Orton has thrown 6 touchdowns and 3 interceptions in his two career games against the Birds.
"We have Kyle Orton here for a reason, veteran quarterback who started over 80 games in the National Football Leage...right now, we have a quarterback who's getting treatment for an injury he had in the ball game. Kyle knows he has to be ready. Kyle prepares that he's the starting quarterback each and every week," Garrett said.
Earlier in the season, the Cowboys defeated the Birds 17-3 in Philadelphia on October 20.
The Eagles defeated the Chicago Bears Sunday night 54-11.
Garrett says the Cowboys' task at hand now is to prepare for Philadelphia.
"Anytime you score 54 points in a ball game you are doing something right," Garrett said.
ESPN and The Associated Press contributed to this report.