Answer:
No, Senator Thompson can not do this as all matters dealing with money must start in the U.S. House of Representatives.
Step-by-step explanation:
The rule comes from the U.S. Consitution, Article I, Section 7, Clause 1: All Bills for raising Revenue shall originate in the House of Representatives; but the Senate may propose or concur with Amendments as on other Bills. If the bill was drafted in the U.S. House and passed the U.S. House Subcommittee, then passed by the full U.S. House, Senator Thompson could go around and ask other Senators to vote for the Bill, but he could not have written the Bill and have it start in the U.S. Senate.