Cross another headache off the House Democratic whip list. Rep. Luis Gutierrez (D-Ill.), who was officially opposed to the latest incarnation of the health care overhaul on account of tougher immigration language, announced Thursday afternoon that he will support the package.

Gutierrez had signaled as much on Wednesday, when he said he was taking a “macro” approach to his vote and suggested he could come around if President Barack Obama gave him assurances that the administration would push for comprehensive immigration reform in short order.

His announcement came as the full Congressional Hispanic Caucus announced its endorsement of the health care bill.

“I cannot see that voting against this health care bill is going to bring us any closer to comprehensive immigration reform,” Gutierrez said. “I do see that a success and a victory on health care will allow this president to be strengthened and to be able to carry out with more political capital our ultimate goal.”

The Chicago Democrat has been in extensive talks with Obama and administration officials about pursuing immigration reform. If achieved, that legislation is expected to render moot the concerns of Hispanic lawmakers about the ban the health care bill would impose on illegal immigrants buying their own coverage through new insurance exchanges. But Gutierrez declined to say whether the president had offered specific pledges about moving such a bill. “Time will tell,” he said.