I dont know any Republican is for open borders and that anyone that crosses can just stay forever. I dont think anyone is proposing that as a proposal
The Senate bill says give us amnesty now and we'll get around to enforcing the law, we promise. It brings in at least 66 to 100 million people in the next 20 years with the guarantee of unending, unlimited chain migration. If that's not open borders it's the closest thing to it.