Chris Wallace presses Miller on this point---asking him multiple times why Miller believes these benefits to be unconstitutional---in part because Miller doesn't really want to answer this question. He looks somewhat uncomfortable and first tries to evade this topic entirely by talking in general terms about the size of the federal government. It's understandable why Miller doesn't want to focus on this matter: in the current economic climate, federal unemployment benefits are distinctly more popular than, say, Obamacare. (A disclaimer: the popularity of something does not reflect on its Constitutionality.)
Republican John Raese is running to replace Robert Byrd in West Virginia. He's walking a very different line about unemployment benefits. He's quoted in the National Review, saying,
“Government has to have a little soul to it. There’s nothing worse than to lay people off, and I’ve had that experience. . . . As long as you have unemployment insurance that is revenue-neutral, I don’t have a problem with that. I just don’t like it when they start printing money.”A couple points arise in this contrast. The first is that it gives insight into the ambition of some so-called "Tea Party" candidates, who critique not only the excesses of the past few years or of the post-1960s welfare state but the whole of the New Deal's legacy.
The second is a hunch that many more Republican candidates will be following the example of Raese in talking about unemployment benefits than taking Miller's stance.