Anyone who has married a U.S. citizen and in this way come to live in the U.S. and become a citizen themselves is extremely lucky. The benefits are obviously quite substantial, and indeed, this is why marrying foreigners to help them get a green card or become a citizen has itself become a substantial industry. Therefore, I believe that anyone who is in this position should absolutely have to pay U.S. taxes, assuming that they're living and working in the U.S.
YES. If they live here and work here, then of course they should! Everyone who lives in our country should, regardless of their citizenship. It is a part of living in our frikking country. Do they really NOT pay taxes? How unfair for all of us who work so hard!
If a foreign man marries a US woman, but for some reason still maintains his permanent residence outside of the US, then no he shouldn't pay taxes here. But if he's set up his living situation in the US with his wife, and works in the country, then he would be treated just like any other working citizen of the US, I would think.
If a foreigner marries an American citizen, that does not mean they owe the U.S. Government any money. If someone is not themselves a citizen of the U.S., and they do not live in the U.S., there is no reason for them to pay taxes, no matter who their spouse is.