TMZ broke the story ... Terrell issued an ultimatum to the Wranglers -- 1) cut him a $160,000 check for 4 games he wasn't paid for, and 2) apologize for saying Owens blew off a team charity event at a children's hospital. If the Wranglers don't comply, T.O. has vowed to sue.

Now, sources tell us the Wranglers aren't budging -- refusing to pay Owens the 160k or issue a mea culpa.

We're told things have gotten downright nasty, with Wranglers owner Jon Frankel accusing Owens of blowing off 4 additional team events ... something T.O. vigorously denies.

Now, T.O.'s tightening the screws -- claiming if the Wranglers don't pony up by the end of business today, he's filing suit.