Sens. Bob CorkerRobert (Bob) Phillips CorkerTrump's GOP impeachment firewall holds strong George Conway hits Republicans for not saying Trump's name while criticizing policy Trump announces, endorses ambassador to Japan's Tennessee Senate bid MORE (R-Tenn.) and John HoevenJohn Henry HoevenBottom Line Poll: McConnell is most unpopular senator McConnell ups pressure on White House to get a budget deal MORE (R-N.D.) are expected to propose language as early as today that would require 700 miles of border fending to be built and a doubling of border agents. But Sessions said there are several questions he has about the pending language, such as whether it would provide for legal status before the border measures take effect, whether the fence would have to be built first, and whether it would require a biometric entry/exit system at all U.S. borders.

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Other questions he has are how to handle delinquent taxes and domestic violence cases involving illegal residents. But Sessions said the Senate appears to be on track for just approving the Corker-Hoeven proposal on border security and shutting off debate on several of these other issues.

"We're told today … that we still will see today a magic amendment, the amendment to fix everything, that we can just relax and go home and take a good nap because we've got an amendment that's going to fix all the problems in the legislation," Sessions said.

More broadly, Sessions said the sudden consideration of tougher border measures shows that supporters of the bill realize that they need to improve the legislation after first defending it as a finished product. He said the first draft of the bill would have spent $6.5 billion on border enforcement, but the Corker-Hoeven language might spend as much as $38 billion.

"That's odd because we were told when the bill was announced that this was the toughest legislation ever, and it fixed everything," he said. "Now the sponsors of the bill have realized that they've got a lot of problems."

Despite his criticisms, Sessions may be part of shrinking minority in the Senate, as the Corker-Hoeven language could end up getting as many as 15 Republicans to support the immigration bill, which could allow the bill to pass the Senate with 70 votes.

On Friday morning, Senate Majority Leader Harry ReidHarry Mason ReidTrump thanks Reid for warning Democrats not to underestimate him Reid warns Democrats not to underestimate Trump Harry Reid predicts Trump, unlike Clinton, won't become more popular because of impeachment MORE (D-Nev.) said the Senate would debate the immigration bill until 2:30 p.m., when he hopes to have a procedural announcement on the new amendment.

Reid has said he would look to close down debate on the bill in the coming days — possibly over the weekend — in order to hold a vote on the bill next week.