They have lost three of their last four games and six of their last 11 dating back to last season, when they opened 12-1.
The season and the team's flagging playoff hopes are now on the line with games against the Buccaneers and the Giants before the bye week.
Owner Jerry Jones is disappointed, but he said Phillips will stay until the end of the season at least.
But all bets are off if the Cowboys lose the next two games and go into the bye week 4-5.
Phillips said he understands the nature of the situation but will go about his business of trying to turn things around.
"Well, I think that's common," he said of rumors about his job stability. "I've been in the league a long time. That's common. That stuff gets talked about. That's not going to (affect) how we prepare for this game this Sunday."
The players are also trying to tune out the talk of Phillips' job security.
"I don't know," linebacker Bradie James said. "I really don't know what to say about it all. All I know is we have to come back and bounce back. There's a lot to be said, and usually the way this league works, the head guy is the first guy to get the blame. But it all runs downhill, so we've just got to get ready."
MONDAY LEFTOVERS: CB Adam Jones was admitted to an out-of-state alcohol-rehab treatment center Monday. Jones was suspended indefinitely by the league last week for violating the NFL's personal-conduct policy. The league mandated that he undergo treatment if he hopes to get reinstated. Commissioner Roger Goodell will re-evaluate Jones' situation after the Nov. 16 game against the Redskins.
--QB Tony Romo will be a game-time decision for Sunday's contest against Tampa Bay. Romo missed last week's game with a broken pinkie. He was ruled out in pregame warmups against the Rams because he had problems with his finger and gripping the ball.
His timetable might be accelerated this week because the team is in desperation mode.
"He threw it all right when we went out early, and we thought it would be fine, then he had a little more problem there," coach Wade Phillips said of the Romo decision before the game. "It was a concern, and then we got in a situation where it really wasn't prudent to put him in anyway."
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