Cruz and Rubio say they will support nothing but a full repeal.
The bill would have blocked refugees from nations with "terrorist-controlled territory."
"I've been disappointed by Republican fear mongering and bigotry," he said.
But the Iowa Republican added a hold on a top State Department nominee.
He wants to block new refugees from getting access to public benefits.
Jordain Carney 11/18/15 07:25 PM EST
Davis County Attorney Troy Rawlings, a Republican, is investigating the Senate minority leader...
Sen. Sherrod Brown (D-Ohio) said Republicans are holding national security nominations "hostage."
But the bill faces an uphill battle in a divided Senate.
He said the bill passed by Congress "needlessly created more vulnerabilities."
The Senate also named its negotiators for the talks.