The Senate voted 54-43 to table the amendment, proposed by Sen. John Cornyn, R-Texas, which has been seen as crucial to get more GOP support for the legislation.
Sen. Marco Rubio, R-Fla., a member of the "Gang of Eight" that crafted the measure, broke from his fellow GOP Gang of Eight members by voting against tabling Cornyn's amendment. Sens. John McCain and Jeff Flake, both of Arizona, and Lindsey Graham of South Carolina voted to table Cornyn's amendment, effectively killing it.
Cornyn's "Results" amendment would have required border enforcement standards in the Gang of Eight bill be met before anyone could be granted permanent legal status.
"My amendment is designed to turn border security rhetoric into reality. More specifically it would have a trigger," Cornyn said before the vote. "The difference between my amendment and their bill is that their bill promises the sun and the moon when it comes to border security but it has no trigger mechanism."
The Corker-Hoeven alternative to border security provisions in the Gang of Eight's bedrock immigration bill would call for a "border surge" plan that would double the number of U.S. Border Patrol Agents and ensure 700 miles of fence is completed along the U.S.-Mexico border.
House Speaker John Boehner, R-Ohio, told reporters he hadn't seen the alternative proposal but said border security -- and confidence the border is secure -- is necessary "before we begin to go down this path of addressing both the legal immigration issues and the illegal immigration issues."
Regardless of the Senate's action, the House is "going to work its will," Boehner told reporters Thursday.
"Our members, when we get back after [the] July 4th [recess], the Republican conference is going to have a special conference where there's going to be a broad discussion of this," he said. "And out of that, hopefully we'll determine, you know, what the way forward is."
Boehner said he hasn't reviewed the Congressional Budget Office report that calculated the Senate bill would cut the federal deficit by $897 billion in the next two decades but said he asked Budget Committee Chairman Paul Ryan, R-Wis., "to do his own analysis of what they've done."
" But I want to get to the bottom of it, because it's -- if, in fact, those numbers are anywhere close to being accurate, would be a real boom for the country," he said.