I hope you're still reading your answers since I see you left this question a couple of weeks ago.
The prevailing wisdom is and has been amongst the attorney's I have spoken to about this has been if both parties are working toward and agreement it is common for them to work through the written deadline if they think there is a chance to reach a "meeting of the minds" on the other hand, if the parties are not getting their minds to meld then the date given in writing is the date that negotiations MAY end. It does not mean they have to END but each party becomes free to pursue other deals. In a Sellers market their might be another buyer ready, willing and able to purchase the property so then the SELLER is free to pursue that other buyer. In Today's market, especially for an out of town BUYER the deadline permits the BUYER to find a different property and enter into a new contract.
The information you have about a contract not existing untill all parties have reached an agreement and that agreement has been delivered to each party is correct. Then and only then do you have a contract.
Prior to that we consider the deal to be in the negotiation stages.
During the negotiation stage we often toss changes to the written deal back and forth verbally and when we get agreement to all the changes we then put the changes to writting and have all parties initial and date the change.
There are "Time Lines" such as inspections, repairs, etc., which because they are performed by 3rd parties which might not work on week-ends and holidays there are those exceptions. Real estate professionals should be expected to complete the transaction on any day of the week. Somewhere, very early in my career i learned a new 4 letter word "ESSH" . It stands for Evenings, Saturdays, Sundays and Holidays. Agents that don't work at those times need to have an assistant or partner that does.
Caveat: I am NOT AN ATTORNEY..and I don't practice law, I am just a relay and I know how we get deals done here.
I used to practice in the Upper midwest in MN and it was very much the same
JD "Dan" Weisenburger, GRI
Vanguard Realty, Inc., GMAC Real Estate