Jessica Simpson almost ruined Tony Romo's NFL career -- but he saved himself when he dumped her and ended their "tumultuous relationship" back in 2009 ... so says .
The "Undisputed" host was discussing his own love, hate relationship with the Cowboys on FS1 Thursday morning -- when he went in on Jessica and their off-the-field drama nearly had NFL ramifications.
Bayless -- who basically eats, sleeps and breathes Cowboys -- says Romo himself who has talked about how the relationship with the singer was bad for him.
"It was just tumultuous.