Should undocumented workers be eligible for Obama-care?

This is quite fascinating:

What a complicated mess! Well, so long as these people are working in America, then don't they deserve the same benefits as any other worker? For example, if an ordinary worker under the law receives special protections against abusive labor practices, then this applies even to undocumented workers. So shouldn't undocumented workers be eligible to the same benefits? Hey, but then why use undocumented workers if they're going to cost so much?  ...

Again, what a complicated mess. In general, I don't support government sponsored healthcare. Not only does it lead to messes like this, but it actually sets up barriers *against* immigration. Any benefit that is bestowed upon labor via the government will raise the bar for those who want to immigrate into a country, and to the extent that the employer is somewhat responsible for the benefit, it will increase the number of employers who try *not* to "do their part" by using undocumented laborers.

Does that make sense?