The NFLPA would be stupid to allow it. That would give a huge lever to the teams.
"Look, we are offering you a contract for $x. We need a decision before the draft tomorrow. If you don't want it, player y has already said they would take it. You'll get less than this anyway because of the slotting process."
It is not as big of a deal with the first pick, because there are weeks to mull things over. With a deadline of days or even hours, that becomes too big of an advantage for the owners.
What really needs to happen is a wage scale for the first contract based on draft position with lots of performance incentives.
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