Yes, CT was passing a law about short stays end of last year to curtail trafficking, I don't know if it is still alive or if motels are ignoring.
As for short stays, the web sites have not achieved much traction, except for large cities.
You have not detailed where you want your short stay to be near?
Alexander sounds like a good tip, it was not on my radar.
My advice is:
Google map, it shows the price for most lodging, call up the sub 100/night places, and ask about short term rates.
dont be shy you are a salesman on the road and just need to lay down for a few hours.
Also, ask about CASH ONLY, if you are worried about a paper trail of CC.
Also very few will NOT take a copy of your photo id.
Also, depending on your situation, getting a discount room via online may be same/less $ then the short time rate.
NEVER, give the room to the provider if you are done with it, have a story that you are using it later.
WATCH OUT for bed bugs, really!