The debate over health care just added a new wrinkle. Rep. Luis Gutierrez (D-IL), a key ally of Barack Obama’s from Illinois, said today that he would find it “extremely difficult if not impossible” to vote for a health care bill that included the restrictive and discriminatory measure on undocumented immigrants that appears in the Senate’s version and has the White House’s support.

Gutierrez, a leader in the Congressional Hispanic Caucus, objects to a provision in the Senate bill that would bar all undocumented workers from participating in the insurance exchanges, even with their own money. The White House has repeatedly expressed support for this measure, as recently as yesterday, when Health and Human Services Secretary Kathleen Sebelius reiterated the President’s position.

Here’s Gutierrez’s statement, passed on by his office:

“It is no secret that I have been critical of proposals that would exclude our nation’s hardworking immigrants from the health care exchange, and I would find it extremely difficult if not impossible to vote for any measure that denies undocumented workers health care,” said Rep. Gutierrez. “If we bar the immigrant community from buying private insurance with their own money, we relegate them to emergency room care at the highest cost to taxpayers and deny them the important opportunity to demonstrate their commitment to a healthier America. Immigrants are prepared to pay into the system. I hope my colleagues in the Senate will defer to the language in the House bill on this issue and bear in mind that excluding immigrants from the private marketplace runs counter to the very goals of health care: containing costs, increasing the use of preventative care and streamlining the health delivery system.”

The White House has said that undocumented workers would still be able to buy private non-exchange insurance, but that market is unlikely to exist, especially if the exchanges work as intended, providing a cheaper product and more choice for those who do not get insurance coverage from an employer.

Religious groups as well as some Senators like Robert Menendez (D-NJ) object to the Senate provision, but it’s unclear whether or not Menendez can find 60 votes to amend the bill. That leaves the conference committee, and at least one House member is against the bill with the Senate language on the undocumented. I’m assuming he’s not the only one.

With these multiple issues piling up – abortion, the public option and now immigration – finding an acceptable compromise will represent a huge challenge.