The power of mutual deadlines.
Here is your problem: You are deadlocked. There appears to be no end in sight. You are smart enough to know that if you impose a deadline it could work against you. Deadlines run the risk of making you concede too much. Likewise if you have a real deadline you are loathe to let the other side know it because they could use it against you. This is the standard logic in play when we discuss deadlines.
However, consider this. Setting a deadline might actually give you the upper hand. Studies have shown that if you reveal a deadline to the other side you can motivate the other side to make a concession with the goal of getting a deal. A seemingly endless negotiation can be moved off dead center by laying down a real deadline. It is important that you fully commit to the deadline.
The understanding that the decline applies to both parties equally can avoid costly stalling tactics. In order for a deadline to be an effective tactic it has to have equal consequences for both sides.