On Monday, Senate Majority Leader Harry ReidHarry Mason ReidLobbying world Senators fume over fight to change rules for Trump's nominees After Dems stood against Pompeo, Senate’s confirmation process needs a revamp MORE (D-Nev.) filed cloture on the comprehensive immigration reform bill. Grassley said it’s now “unclear if any more amendments” will be voted on.

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The Senate is considering the Border Security, Economic Opportunity and Immigration Modernization Act. Reid has said he wants work completed on the bill by the July 4 recess.

The bipartisan group of eight senators, known as the Gang of Eight, introduced S. 744, which would create a pathway to citizenship for illegal immigrants already in the country, toughen border security, create a guest-worker program and boost high-skilled immigration.

Republicans, including Grassley, have complained that the bill repeats mistakes made during the last major immigration reform in 1986, when people were given citizenship before border security enforcement measures were in place.

Later Monday, the Senate will vote on whether to end debate on a substitute amendment from Senate Judiciary Committee Chairman Patrick LeahyPatrick Joseph LeahyCongress should build on the momentum from spending bill Overnight Tech: Zuckerberg grilled by lawmakers over data scandal | What we learned from marathon hearing | Facebook hit with class action lawsuit | Twitter endorses political ad disclosure bill | Uber buys bike share Overnight Cybersecurity: Zuckerberg faces grilling in marathon hearing | What we learned from Facebook chief | Dems press Ryan to help get Russia hacking records | Top Trump security adviser resigning MORE (D-Vt.). His amendment included the “border surge” language from GOP Sens. Bob CorkerRobert (Bob) Phillips CorkerGOP anxiety grows over Trump’s Iran decision Trump backs Renacci in Ohio Senate race The Hill's 12:30 Report MORE (Tenn.) and John HoevenJohn Henry HoevenLobbying World Worried GOP views Trump trade war with angst Conservatives fear trade war could cripple tax cuts message MORE (N.D.). 

In the underlying bill, an E-Verify system and entry-exit system at air and sea ports must be in place before anyone is given a green card. The amendment from Corker and Hoeven would also make require construction of 700 miles of Southern border fencing, the purchase of more than $3 billion in new technology for border security and the hiring of 20,000 more border patrol agents mandatory before green cards are issued.

"It’s quite obvious that I’m going to vote against this amendment," Grassley said. "It does little to address the legalization-first philosophy."

Corker said his amendment has “five tangible triggers” that Republicans have demanded, taking power out of the hands of the Department of Homeland Security to waive border security provisions. The trigger must be in effect 10 years after the bill is signed into law.

Adoption of that amendment is viewed as critical to attracting more Republican support for final passage, which the bill’s authors want in order to put more pressure on the House to take up the legislation.

But Grassley said the amendment is still weaker than current law.

“We were told we were going to secure the border. Well, we’re going to secure the border after legalization,” Grassley said. “But legalization is going to take place before any plan is in place.”