With a tentative deal on a crucial border security amendment in place, Senate immigration-reform negotiators on Thursday were vetting the proposal with colleagues on both sides of the aisle and the White House.

Sen. Charles, Schumer, D-N.Y., was presenting the amendment to White House officials, as well as business and labor representatives, a knowledgeable source confirmed. If the deal is acceptable to all parties, look for the principle authors of the amendment, Sens. Bob Corker, R-Tenn., and John Hoeven, R-N.D., to introduce it on the Senate floor, sometime Thursday afternoon.

At that point, Schumer would head to the Senate floor to speak in support of the amendment, signaling that the majority Democrats are on board with the proposal.

Sen. Marco Rubio, R-Fla., who along with Schumer is a key member of the "Gang of Eight," was asked by the Washington Examiner if the Corker-Hoeven agreement was going to hold and if it would satisfy concerns about border security that he relayed earlier.

"We'll know more in a few minutes," he said.