Sen. Lindsey GrahamLindsey Olin GrahamGraham asks colleagues to support call for China to close wet markets Justice IG pours fuel on looming fight over FISA court Trump says he's considering restricting travel to coronavirus 'hot spots' MORE (R-S.C.) on Sunday said the Senate is "on the verge" of getting 70 votes to pass the Gang of Eight's immigration bill, crediting the recent deal on border security language with winning more GOP votes.

"The bill will pass. I think we're on the verge of getting 70 votes. That is my goal," Graham said on "Fox News Sunday." "We're very, very close to 70 votes. The Hoeven-Corker amendment I think gets us over the top."

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The Senate is slated to vote on the border security amendment by Sens. Bob CorkerRobert (Bob) Phillips CorkerMcConnell, Romney vie for influence over Trump's trial RNC says ex-Trump ambassador nominee's efforts 'to link future contributions to an official action' were 'inappropriate' Lindsey Graham basks in the impeachment spotlight MORE (R-Tenn.) and John HoevenJohn Henry HoevenGOP senators urge Saudi Arabia to leave OPEC GOP divided on next steps for massive stimulus package Overnight Energy: Democratic lawmakers seek emissions reductions in airline bailout | House Dems warn Trump against oil industry bailout | GOP senators ask Saudis to stabilize oil market MORE (R-N.D.) on Monday. The amendment is viewed as key to securing more GOP votes for the bill.

Senate Majority Leader Harry ReidHarry Mason ReidGOP embraces big stimulus after years of decrying it Five Latinas who could be Biden's running mate Winners and losers from Super Tuesday MORE (D-Nev.) wants to finish work on the sweeping immigration bill this week and hold a vote to end debate on the underlying bill on Thursday.

Graham, a member of the bipartisan Gang of Eight, called the Corker-Hoeven amendment "the most aggressive attempt to control the Southern border and regain our sovereignty."


He stressed that Republicans will be blamed if the bill fails to pass the Senate, which would continue to drive Latinos away from the party. The GOP is seeking to court more Latino voters after an overwhelming majority of them voted for President Obama in the 2012 election.

"If it fails, then we are blamed for its failure," Graham said. "Our party is in trouble with Hispanics, not because we're conservative, but because of the rhetoric and the way that we've handled this issue."

"I want to get reattached to the Hispanic community…pass comprehensive immigration reform, grow this party," he said. "The Hispanic community is very close to our values, but we have driven them away over this issue. Let's fix this problem for the good of the country and for the good of the party, and this bill does that."

Sen. Mike LeeMichael (Mike) Shumway LeeJustice IG pours fuel on looming fight over FISA court Senator Tom Coburn's government oversight legacy Trump on Romney's negative coronavirus test: 'I am so happy I can barely speak' MORE (R-Utah), an opponent of the bill, however, criticized the Gang of Eight measure for wrapping the most "contentious" issues on immigration into a single bill that spans more than 1,000 pages. He praised the House's approach of tackling immigration in a piecemeal fashion.

"What's making this contentious, what's making it politically divisive, is the Senate Gang of Eight has insisted on wrapping all of these issues up into one 1,200 page bill," Lee said also appearing on "Fox News Sunday." "They're putting the single most controversial…issue, that of amnesty and ultimate citizenship, into a 1,200 page bill."

Lee also said the Senate bill lacked teeth on border enforcement and few members have had the chance to fully weigh the merits of the Corker-Hoeven amendment. However, he predicted the bill will ultimately pass the Senate.

"They told us [the bill] would be tough but fair, and it's neither. It's not tough on those who have broken the law and it's not fair for those who have been patiently waiting their turn in line to come to this country legally," Lee said.

"Look, we all want immigration reform, but this bill is not the vehicle for getting there," he said.