Canceling SLS would mean losing jobs, yes. But that's not because of some sort of Boeing monopoly on space (they're obviously not a monopoly in that area), it's because the program is designed to be inefficient, with tons of 3rd party suppliers intentionally spread across the entire country, and tons of extra red tape to justify creating more jobs. They and other old school defense contractors specifically advertise these projects with the promise of creating jobs in all 50 states.
I'd disagree on the claim that the senators have fantastically small power on this matter, a single senator was capable of holding back in-space refueling tech for at least a decade under threat of canceling the entire space technologies program (because if you can refuel in space, even launching several medium lift disposable rockets is more efficient, and that'd mean no need for SLS, affecting jobs in his area).