"It depends on how it is crafted," Tester says. "Although it is kind of de-facto citizenship right now, so it would be nice to have a solution."
For some Republicans, it seems no amendment will be radical enough to win their support.
Sen. Jeff Sessions, R-Ala., who has been one of the most outspoken advocates against the bill, hinted Tuesday he may filibuster the legislation because it is moving too fast.
"I think the legislation in the light of day is going to have real trouble, and frankly my concern would be some fig leaf amendments that do not fix the weaknesses in the bill would be seen as sufficient," Sessions says.
Sen. Lindsey Graham, R-S.C., a member of the gang of eight, recognizes that his delicately crafted bill is still in danger of crumbling under the weight of too many competing interests. But he offers a specific warning to his GOP colleagues, encouraging them to tread lightly as they push for tougher amendments.
"If we are not able to pass immigration reform in 2013 and it is the Republican Party's fault, we are dead in 2016," Graham says. "If we look for reasons to back out, or the bill fails and it is seen that we are not practical, we are not trying to solve the problem, we will pay a heavy price."