From TPM:

“We really thought we’d resolved this question of people who are here illegally, but as we reflected on the President’s speech last night we wanted to go back and drill down again,” said Sen. Kent Conrad (D-ND), according to Time. The incident reportedly has led Finance chairman Max Baucus to insert a provision in his legislation to require participants in the health insurance exchanges to provide proof of citizenship.
Two things remain unclear. First is whether non-citizens would be barred, by this provision, from receiving federal subsidies, or entering the exchanges altogether. That’s the difference between an inconvenience and actually barring undocumented residents from buying buying health insurance.
Second, is how progressive members of Congress and immigrant groups will respond to the news. We’ll let you know the answer to both questions.