The White House rejected on Tuesday a top Republican senator's suggestion that immigration reform was "dead" in the Senate this year.

White House Press Secretary Robert Gibbs said that President Barack Obama and other administration officials would continue reaching out to lawmakers in both parties to gauge the extent to which immigration reform legislation is attainable this year.

"I, not surprisingly, would likely disagree with that characterization," Gibbs said during his daily press briefing in response to Sen. Lindsey Graham's (R-S.C.) claim last week that a bruising healthcare battle made immigration reform all but impossible in the Senate.

Graham had been partnering with Sen. Chuck Schumer (D-N.Y.) on potential comprehensive immigration reform legislation, about which they met with Obama earlier this month.

But the South Carolina Republican said that little political will was left to move forward on a politically thorny issue like immigration.

"This is not an issue that's going to be decided by just getting all the Democratic members to support immigration reform," Gibbs said. "There have to be Republicans that come aboard, too."

"Those conversations, the president is likely to have with Republican members in the near future," the press secretary added. "And we'll gauge whether or not it's possible to move forward on this issue."

Graham has challenged the administration to write its own immigration bill to move through the Congress, a challenge which Gibbs sidestepped on Tuesday, noting that the president finds a number of aspects in the Schumer-Graham proposal "greatly appealing."