Senate Majority Whip Richard J. Durbin says that he supports increased transparency when it comes to National Security Agency surveillance programs, but he cautioned against getting into that issue during the immigration debate.

“That would be a serious mistake. I would resist that — whatever they want,” the Illinois Democrat told reporters Tuesday in response to a question about the chances that NSA amendments may surface as the bipartisan immigration overhaul moves on the Senate floor.

Because the Senate has no general germaneness requirement until cloture, any senator may try to offer any amendment to the measure. Such a move could put Democrats in a tough spot. Majority Leader Harry Reid, D-Nev., has pledged an open process, but he tends to stop the spigot of amendments when they go too far afield.

Durbin has supported past efforts at increased transparency of intelligence, however.

“These bills are coming very quickly, and I’ll try to keep up with them, but I think more transparency would re-establish American confidence in our efforts to keep us safe,” he said.

Sens. Jeff Merkley, D-Ore., and Mike Lee, R-Utah, led a group of eight senators Tuesday morning in unveiling a measure to declassify Foreign Intelligence Surveillance court opinions.

But as expected, Edward Snowden, the man who actually leaked the information about the NSA programs, has had very few lawmakers saying anything favorable. Lee told reporters that, by all accounts, it looks like Snowden broke a number of laws.

Others agreed. “My general feeling about people like this when they disclose classified information designed to make us safe, emboldening our enemies and making the rest of us less safe, I don’t find anything he did noble at all,” said Sen. Lindsey Graham, R-S.C.

Even Sen. Rand Paul, R-Ky., one of the few senators to come to Snowden’s defense, wants to keep the attention off of him and on the government. Paul told CBS that he viewed Snowden’s own criminal liability as a less important issue, with the scope of the NSA programs related to phone records and electronic communication deserving the Senate’s and the public’s attention.

“I think he’s sort of a side point,” Paul said. “I think the real point is that the Bill of Rights are being violated. Our privacy is being violated. Really, no government should do this, and we need to obey the rules.”