an unpleasant operation

Mike Wallace: With the wedding march these days marching to a different drummer, Andy's perplexed about why the government insists on getting into the act.
Andy Rooney: It's hard to guess what the issues are going to be in an election year. Who would have thought, a year ago, that we'd be arguing over gay marriages? President Bush has his solution.
President Bush: Today I call upon the Congress to promptly pass, and to send to the states for ratification, an amendment to our Constitution, defining and protecting marriage as a union of a man and woman as husband and wife.
Andy Rooney: Mmh, I don't know. Most Americans disapprove of gay marriage, but if Congress gets into the marriage business, it'd better look into all marriages, not just gay ones, because marriage is in big trouble. More than half of all marriages in the United States are ending in divorce these days. In some states it's even higher. In the year 2000, seventy-one percent of all married people in Oklahoma got divorced. There're so many divorces that they make the wedding business look ridiculous: the organ music, the vow "'til death do us part", the announcement in the newspaper, the bridal gown. Where are the divorce announcements in the paper? How come a woman getting divorced doesn't wear a gown and have a party with a cake? Where's the church, the minister, the priest in a divorce? So, forget making gay weddings illegal, Mr. President. If you want to make marriage more stable, make divorce illegal. (If) people knew they couldn't get out of it, they'd be more careful getting into it. A man who leaves his wife with kids to take care of, so she has to go on welfare, would be required to undergo an unpleasant operation to make sure that never happened again.

Could you tell me what 'an unpleasant operation' refers to, what 'undergo an unpleasant operation' means, please? Thanks.