Four lines that should make you slow down
None of them proves someone is dishonest. Each one takes away your time or your proof.
Most contractors are honest people who are bad at paperwork. A few are neither. These four lines don't prove which kind you're talking to, but each one should make you slow down.
"This price is only good today."
Material prices do move, and a quote can reasonably expire in a few weeks. A price that expires when the salesperson leaves your driveway is pressure, not pricing. A fair price is still fair tomorrow.
"Cash only. No receipt needed."
Paying in cash isn't the problem. Having no record is. Without a receipt you can't show what you paid, and you may have trouble with a warranty claim later.
"We don't need a written contract."
You do. It doesn't have to be long. It has to say what gets done, with what, for how much, and when. A contractor who resists writing that down is asking you to rely on memory, and memories differ when money is involved.
"We have leftover materials from a job down the street."
This is one of the oldest door-to-door lines there is, usually for driveway sealing, roofing or paving. Real leftovers go back to the supplier or on to the next scheduled job.
What to do instead
Take a day. Look up the company's license if your state requires one. Get one more quote for the same scope. If the first offer was a good one, it will survive the comparison.