It is true they are powerful, and control every bill that reaches the Senate (and of course any non-spending bill they create), but they can't pass their own spending bills. They can only hold them up, or amend them and send back to the House to try to get them to agree. They could try drafting one but the House has zero obligation to do anything with it.

I do get the point you are making though. Senate leaders are very powerful, and Washington has a long history of bribery, deals, and strong-arm tactics. A Senate leader could refuse to consider anything from the House unless they do his bidding, or even offer to name a post office in BFE for the House member. It happens. It might even be legal, but it shouldn't.

Oh - Schoolhouse Rock was great and should have never gone away. But:

“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.” — Article I, Section 7, Clause 1