Senate Minority Whip John Cornyn (R-Texas) said he was "encouraged" by the progress on a bipartisan immigration bill and is open to voting for it depending on its final details.
"I'm encouraged by what the so-called 'Gang of Eight' including what Sen. Durbin, Sen. [Marco] Rubio [R-Fla.] and others have come up with," he said on “Fox News Sunday” during a joint appearance with Senate Majority Whip Dick Durbin (D-Ill.).
"I believe border security is absolutely critical to this picture. So much of it is regaining the public's confidence that the federal government is actually doing its job, so until that confidence is restored on based on the basis of what the legislation provides, I would have difficulty supporting it," he said.
"But having said that, I want to read it, I want to go through the regular process on the Judiciary Committee and on the floor and I'm open certainly to supporting immigration reform."
Cornyn sounded a different note on gun control, however.
Sens. Joe Manchin (D-W.Va.) and Pat Toomey (R-Pa.) have struck a bipartisan compromise on closing background check loopholes as the Senate begins debate this week on a gun control bill.
While the background check deal is expected to get a vote this week, its prospects appear up in the air.
Cornyn was one of 16 GOP senators who voted against closing debate on the Senate gun bill last week and said he doubted more gun restrictions would prevent violence.
"I'm focused like a laser on the mental health component," he said when asked about his meeting with the parents of children murdered in Newtown, Conn., who have been advocating for stricter gun control.
"I'm not for symbolism over substance," he continued after arguing increased background checks wouldn't have prevented the Newtown killings or other mass murders that have occurred in recent years. "I think we can't just pat ourselves on the back and say we're going to pass some enhanced penalties for trafficking or other issues or background checks when they don't really go to solve the problems that solve these terrible tragedies."
Durbin, however, argued for the Manchin-Toomey plan.
"We've got to ask the basic question: Should we try to keep guns out of the hands of felons and people so mentally unstable they shouldn't own a firearm? If the answer is ‘yes,’ Manchin-Toomey is a step in that direction," he said.
Neither Durbin nor Cornyn would say they had the votes to win on the measure, a sign that the vote may be close. Toomey said later on CNN that it was an "open question" how the vote would go, and predicted it would be "close."