Dan is on the mark! You have an agreed upon contract that both parties need to abid by unless the parties involved agree to and sign an "addendum" changing the terms of the agteement.
It's time to communicate and negotiate to see if there are terms that will help both parties with their individual dilemma. I would want to know what is causing the seller to not be able to abide by the terms of the agreement? They may be finding themselves in the same situation you are in...without a place to move into after closing.
If they value selling their home, they should be able to come up with a workable alternative that doesn't inconvenience you. Your agent should be all over this and advocating on your behalf.
In the meantime, as a failsafe, it might be advisable to see if you could extend your rental a while longer.....I'm not saying to offer this, only to have a back up plan if needed.......
In Florida, its the buyers who obtain a termite inspection, if that is holding up your closing, could you order a termite inspection?
Here's the situation, you can decline and your contract is still in force. They can decline to cooperate and potentially void the contract and then everyone gets the lawyers involved. Any changes to the terms of a contract must be agreed to by all parties, you can't dictate and neither can they, however from a practical perspective, they could comply with everything and just not move out. Then you begin eviction proceedings and the process takes longer than the extension you need.
What needs to happen here is everyone needs to discuss and negotiate. For example, you can say, "I'll give you the extension in exchange for the cost of daily storage with the moving company, plus the nightly cost of the local Residence in until we close. This gives you a place to stay at no expense and lets them know it's their problem not yours. They can agree, counter offer or just realize they should stay with the original date.
This is just an example, but think outside the box and come up with a workable solution so you don't end up homeless.