Will the United States Patent and Trademark Office contact me directly and request payment?

No. The USPTO will never contact you directly.
With this in mind, note that there are companies that attempt to scam users by searching the United States Patent and Trademark Office database and contacting the owners of Trademarks directly, seeking payment. If you have received a Solicitations, do not hesitate to contact your PTRC to confirm or disregard the notice if you are certain it is not from the USPTO but from a company trying to mimic the government entity.