I’m looking for a phrase that means mission impossible

Solution 1:

If you

paint yourself into a corner

you have made things very difficult or impossible to get out of.

The Vikings have painted themselves into a corner to try to trade the bulk of Kirk Cousins contract.

Solution 2:

You are already verging on something very near to the same meaning. Though it looks like you might have a noun in mind, the use of the phrase/idiom "near to impossible" (verb) or "near-to-impossible" (noun) as a descriptor would fit perfectly.

“The Vikings are engaging themselves in a near-to-impossible task/try/attempt to trade the bulk of Kirk Cousins contract.”

Otherwise, since your question is tagged as a single-word-request, you might use "hopelessness" just as well.

“The Vikings are fooling themselves with the hopelessness of trying to trade the bulk of Kirk Cousins contract.”

https://idioms.thefreedictionary.com/near+to+impossible

https://www.freethesaurus.com/impossibility