An aggressive hunt for votes to pass immigration reform began this week as the Senate agreed to start the lengthy, and likely heated, debate about whether and how to provide citizenship to the 11 million undocumented immigrants currently in the United States.

But backers of reform said merely passing the bill with 50, 60 or even 65 votes won’t be enough to get the Republican House to act on the legislation. Instead, a new goal of a 70-vote über-majority has sent senators, lobbyists, and outside interest groups scrambling to push roughly two dozen moderates from both parties to commit to voting yes or no.

“If we don’t get to 70, we’re in trouble,” Sen. Lindsey Graham (R–South Carolina) told The Daily Beast, stressing that there’s a difference between passing a bill through the Senate and seeing it become law. “If you get 61, it probably dooms it to die in the House, so I think it’s imperative to get close to half our caucus.”

As a member of the bipartisan Gang of Eight that has worked to craft legislation both parties could sign off on, Graham and his allies are working feverishly to build a broad coalition one vote at a time, analyzing what it will take to win over each senator and then pushing him or her to decide through a barrage of meetings, phone calls, and conversations on the Senate floor.

“We say, ‘What would you like to see in the bill to be made better? Is it legal immigration? Is it border security?’ There are some folks I think are very gettable,” Graham said. “We’ll be talking to everybody.”

While undecided senators are getting cornered by their colleagues in Washington, unions, business groups, and advocates on both sides of the legislation have launched multimillion-dollar ad buys to lean on individual members in their home states.

The Service Employees International Union began a seven-figure national ad campaign in favor of the Senate bill this week, while Numbers USA, an anti-reform group, bought ads in 12 swing states, including Nevada, North Carolina, and Ohio, to pressure senators to vote no.

Staffers and activists break the undecided senators into several camps, including red-state Democrats who are up for reelection or have voted against reform in the past, moderate Republicans who are known to buck conservative leaders, and a set of senators in both parties known as “gun refugees” who are likely factoring their recent vote on universal background checks to calibrate how near or far they can stray from their political base on an immigration vote.

Sen. Max Baucus (D–Montana), who is often mentioned as a likely Democratic “no” vote, gave no indication how he would vote on the final bill when asked on Tuesday. “I’m working my way through it. I’m just going through the amendments,” he said. “We’ll have to wait and see.”

Baucus and Sen. Jon Tester both voted against immigration reform in 2007, when Baucus said he could not support a bill that “provides amnesty for illegal immigrants,” while Tester said the 2007 bill would give the undocumented immigrants “a free pass.”

Other possible no votes for the Democrats: Sen. Mark Pryor, who is up for reelection in Arkansas, where Mitt Romney won 60 percent of the vote in 2012, and Sen. Joe Donnelly (D–Indiana), who voted against the DREAM Act in 2010 and ran a campaign ad the same year promising to "deport illegals who commit felonies and eliminate amnesty because no one should ever be rewarded for breaking the law."

On the Republican side, pro-reform advocates point to Sen. Dean Heller as an example of a senator who voted against universal background checks in April, but represents a state that went for President Obama by six points in 2012. Adding to possible pressure on Heller to vote for reform are the changing demographics in Nevada, where the Latino population jumped from 10 to 18 percent of the electorate in the last eight years. Heller called the Senate bill “promising” this week, but added that “certain aspects of the bill need to be addressed.”

Conversely, Sen. Mark Kirk (R–Illinois) voted in favor of background checks, but against debating the immigration bill on Tuesday. While Kirk did not explain his vote, it was widely seen as a move to shift his record to the right before eventually voting for reform.

Republicans in the Gang of Eight are also looking to Sens. Susan Collins and Lisa Murkowski for support, since both have sided with the Democratic majority in the past and also have business interests in their states—-tech interests in Maine and fisheries in Alaska—that are pushing for them to support the Senate bill. Collins is also a cosponsor of a bill to give same-sex couples equal access to immigrant visas.

But to get the Senate bill to the massive 70-vote win they say they need, supporters are working with a block of roughly a dozen Republicans, including Marco Rubio, who voted to debate the immigration bill Tuesday, but say they need significant changes to the border-security measures in the bill to support it in the end. On Wednesday, Rubio offered four additional amendments to deal with everything from requiring immigrants to pay back taxes to limiting their access to “Obamacare” subsidies.

Sen. John Cornyn has drafted a border security amendment to require 100 percent surveillance of the southern border and other major changes to border security before undocumented immigrants could receive legal status. Majority Leader Harry Reid called Cornyn’s amendment a “poison pill,” but Cornyn said he is having “ongoing conversations” with the Gang of Eight to include some version of his amendment in a final package.

“I think if they had 60 votes to pass the bill out of the Senate, they probably wouldn’t be talking to me,” Cornyn said Tuesday. “But they are, which tells me they view this as a way to get the kind of support out of the Senate in a bipartisan basis that would get it some momentum and increase the likelihood of it passing in the House.”

In the end, reform advocates believe a large block of Republicans could support the Senate bill and get it to 70 votes, if only to ensure their own political survival. Senator Graham called not having an immigration bill a potential “death blow” for Republicans in the future.

“From a political point of view, if this bill fails because the Republican Party doesn’t seem to have been practical, doesn’t seem to have been willing to admit that 11 million people are here and they’re not going to self-deport, we’ll pay a heavy price in 2016,” he said. “It will be almost impossible.”