In reply to Dawn G..

Dawn,
Usually private insurance, such as that through an employer, gives much better coverage than Medicaid. If he marries the woman and now has three dependents, he could easily add the family coverage. We Lutherans don't believe that marriage is a "sacrament," as such, so, technically, the state, not the church, makes the marriage.
— Dr. Veith

Dawn,
Greetings. I'm sorry to hear about the difficult decision that faces your son. This is also a common struggle for older folks who receive government benefits of various types as well. The bad news is that, regardless of whether or not we want the government involved, it is. One should not get married surreptitiously and then lie to the state about it. This means that they should get married in the normal order and work to deal with the insurance; as Dr. Veith notes above, if he has private insurance, it's usually better than the public options.
Secondly, this is also where the church can step in to help when and where they are able. Has he spoken to his pastor and the congregation about their needs? I would be surprised if members of the congregation were not interested in helping their brother and sister in Christ who desire to live in marriage. Many hospitals and doctor's offices have programs to help those who cannot completely cover their medical expenses.
Indeed, this will be a burden. But as God's people, this does not surprise us. We confess that Jesus sets before us the way of the cross. It's the way of denying our own desires for the sake of living according to God's Word and will. This is not easy; we will regularly fail. And we fall on the grace of our Lord Jesus Christ, in whom we have forgiveness and life.
Our Lord Jesus Christ did not refrain from coming to save His people because of the suffering He would have to endure. He gladly came to serve. Your son might have to endure hardship and difficulty; but this is precisely what our Lord calls husbands to do for their wives (Ephesians 5:22–33).
Please do not hesitate to email me with further questions.