Yeah they can. Obviously we need to see what the final numbers look like before having hard opinions, but the OSA deal isn't likely to be that bad. The rumors have been 5 years at around $22M. If he gets something in the neighborhood of 5/$110M with about 55-60% of that guaranteed they'll be able to spread that cap hit around with minimal issue and should be able to get out of it after the first couple years if they need to.
From a cap standpoint its probably similar to the
Diggs deal, but probably with a little bit more guaranteed money involved. Diggs so far is only in year 2 of his extension and can be easily cut (if not injured) if the Cowboys wanted to go that way. I get that one hasnt worked out due to injury, but it is more of an injury issue than it is a bad deal. A healthy Diggs would be a steal at his current price. Unless OSA is being unreasonable in negotiations this is a deal that should be more of a risk for Jerrys wallet than the cowboys cap health, and I have no issue gambling with Jerrys money.
The bigger issue is the Parsons extension which you just have to hope he is serious about doing something team friendly and taking a contract more in line with the Nick Bosa 5/$170M (70% guaranteed).