It is being reported that the so-called compromise immigration bill being brought out by the Senate is, in the vernacular, "dead on arrival." Speaker Johnson might not even bring it to a vote in the House.
What people want is a drastic reduction in immigration, orders of magnitude less than currently. It is also what former president and current candidate Trump wants, and most Republicans and Independents agree with him.
Democrats will not sign off on a bill that does what people want, and therefore taking Biden off the immigration hook is too high a price to pay for some minor restrictions in inflows of alien riff-raff. What the Lankford-Murphy-Sinema proposed bill would do is allow quite large flows of asylum seekers and unlimited numbers of unaccompanied children. And it would tie President Trump's hands come 2025.