Actually, there are a lot of Senate Republicans who don’t want to vote for any more stimulus, including the “clean” $1200 checks. This has been widely reported. Mitch is covering for them by claiming they’re just against Pelosi’s pork. The truth is they don’t want to vote for any bill, which is why you haven’t heard Mitch publicly pressuring Pelosi. They’re fine with the House not sending them anything.
Whether that’s the case or not, it’s kind of irrelevant - the whole mess is hung up in the House and there’s nothing the Senate can do about it. Whether or not Mitch is covering for less than kindly disposed senators has no bearing on it at the current time; it will continue to have no bearing until and unless the House produces a bill.