But conservative unrest over the bill has begun to grow. Sen. Marco Rubio (R-Fla.) has taken up the mantle of attempting to sell the bill to conservative critics and rebut arguments made against it. But he's met stiff resistance from voices on the right, such as talk-radio host Rush Limbaugh, who called the bill "suicide" for the GOP.
And Rubio had to swiftly respond this week to a false report that the immigration bill would offer free cell phones to immigrants, what detractors are calling "Marcophones."
On Thursday, Rubio cajoled conservatives to get on board with the bill.
"We all wish we didn't have this problem, but we do," he said. "And we have to fix it. Because leaving things the way they are, that's the real amnesty."
McCain said that the bill is the critical first move in a long process for the Republican Party to repair its broken image among Latino voters.
"A little straight talk here: Republicans have got to compete for the Hispanic vote," he said, using his old campaign catchphrase. "Passage of the legislation … doesn't gain a single vote from the Hispanic community. But what it does it puts us on the level where we can compete in the battle of ideas."
After the conference ended, Norquist predicted the Gang of Eight would succeed, arguing that opponents like Sessions and Vitter, who sunk the last immigration bill in 2007, have been marginalized.
Restrictionists, Norquist said, are people who merely "think of themselves as conservatives."
"If you're a Republican, you look at the business community wants it, the religious community wants it," he told reporters. "Who is the opposition? Who in the modern Reagan Republican Party is a no?"
While Congress has proved itself incapable recently of dealing with major pieces of legislation, the senators predicted this time would be different.
"I am convinced this issue will not fall victim to the usual partisan gridlock," Schumer said. "This bipartisan breakthrough offers a degree of hope."