IRVING, Texas—Tony Romo’s broken little finger has become a big issue for the struggling Dallas Cowboys.

The two-time Pro Bowl quarterback, who wanted to try to play last week despite the broken pinkie on his throwing hand, said Wednesday he now doesn’t expect to play again until at least mid-November.

“I don’t know when I’ll be back,” Romo said. “I think definitely the idea now is to get healthy by that bye week.”

That means Romo would miss at least two more games: Sunday at Tampa Bay and the following week at the rival New York Giants. The Cowboys (4-3), w...

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