"And I'm sure as hell not going to accept an agreement where they get legalization on a pathway to citizenship and then they give me border security, then they give me legal immigration reform," Graham said. "You have to do it together."
Graham also said the Republican Party can't be seen as obstacles to meaningful immigration reform if it wants to appeal to more Hispanic voters, a growing segment of the populace.
"The party has to be bigger than Utah and South Carolina," he said. "Let's fix this for the good of the nation and the good of the party."
Sen. Orrin Hatch, R-Utah, appears to be one of the Republicans likely to join Graham in support of the bill, bolstered by a financial analysis that shows the legislation would reduce the deficit by $890 billion and create a new agreement to double the border patrol and extend a fence along the boundary with Mexico.
But Lee argues the bill's supporters are selling it on false promises.
"They told us that it would be tough but fair, and it is neither," he said. "It is not tough on those who have broken the law, and it's not fair on those who have patiently been waiting in line to come to this country legally."
The legislation would allow many of the 11 million undocumented immigrants to begin a 13-year path to citizenship, with a green card contingent on border improvements and an expanded workplace verification system.
"They will have an earned, hard path to citizenship," said Graham, also noting that these immigrants won't be eligible for a green card until those now waiting for a legal visa receive one. "They can't cut in line. They have to pass two English proficiency exams. I reject the idea of becoming the Mideast or Europe, where we have 11 million people with illegal status who can't become part of America."
Graham said the legislation would stop a future wave of immigration, something Lee also disagreed with. Lee noted the same financial analysis showing a positive economic benefit from the bill and also predicted that in a decade, the United States will still have between 6 million and 8 million immigrants here illegally, mostly for overstaying a visa.
"They promised us under this legislation that illegal immigration will be a thing of the past. It won't."