New Kiwis coach Michael Maguire attended the game at AMI Stadium and will spend the next couple of days in Auckland to assess the fitness of the Warriors' Kiwi internationals, with his side expected to be announced on Wednesday or Thursday.
If fit, Tuivasa-Sheck is a guaranteed selection and a leading contender to captain the side.
But the uncertainty over his fitness, combined with his status as Warriors skipper, mean he may feel an added sense of responsibility to put his health and the club's finals hopes before his international ambitions.
"If he's available then obviously he's selected," said Maguire. "That's a decision that Steve and Roger will have to make but also with the understanding that it's a Kiwi jersey and it's a big opportunity for any player."
Kearney would not be drawn on whether he expected Tuivasa-Sheck to recover in time to make the long-haul trip to Denver.
"My focus is on making sure that we're getting him right to play for us on Friday so we'll see what happens," he said.
If Tuivasa-Sheck does miss the Cowboys match, backline utility Peta Hiku would likely replace him for a third time this season, after filling in against the Sea Eagles and in the round 11 win over Parramatta.
Hiku previously played the first five of his 10 tests for New Zealand at fullback and could again cover the No 1 role for the Kiwis if required.
