Whomever President Obama nominates to replace outgoing FCC Chairman Julius Genachowski, there will be political fallout.

FORTUNE -- There are lots of different issues that the Federal Communications Commission can affect: from media ownership rules to broadband deployment to whether broadcasters must pay insanely large fines for "wardrobe malfunctions" and people swearing during live awards ceremonies. But as observers try to guess who might replace outgoing FCC Chairman Julius Genachowski, the issue they cite the most is net neutrality -- the rules that prohibit Internet service providers from favoring some traffic over other traffic, thereby giving themselves or their partners a competitive advantage.

Or anyway, that was the main concern until Wednesday, when it was revealed that 37 Democratic senators had written President Obama a letter asking that he nominate current FCC commissioner Jessica Rosenworcel to the top post. The request has complicated matters even further for Obama. Rosenworcel would be the first woman to head the FCC. But so would Mignon Clyburn, another female commissioner. She not only has more seniority than Rosenworcel does, she happens to be the daughter of Rep. James Clyburn of South Carolina.

"Obama will have to make somebody unhappy," declares Bryan Fung of the National Journal. "Either he'll have to snub someone related to a key figure in the House, or he'll have to upset a handful of allies in the Senate."

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Or he can decide to make everybody unhappy, except perhaps himself and maybe some of his check-writing business pals, by going with Tom Wheeler, a venture capitalist who donated the maximum allowed $5,000 to Obama's 2012 reelection campaign and bundled at least another $500,000 from other donors. In 2008, he bundled a sum less than that, but more than $200,000, according to the Center for Responsive Politics.

Wheeler was president of the National Cable Television Association in the late 1970s and early 1980s, and he was a lobbyist with the Cellular Telecom and Internet Association from 1998 to 2003. At least until the Democratic Senator's letter came to light, Wheeler was being described as the likeliest choice.

Whomever Obama chooses is likely to be someone who will guard the FCC's current rules on net neutrality, which were enacted over the objections of the panel's Republican members in 2010. Nevertheless, Democratic Rep. Ed Markey of Massachusetts, who is running for a senate seat in that state, made a point on Thursday of demanding that any nominee have an "understanding of net neutrality, an understanding of the non-discriminatory principles that are baked into the Internet from its origin."

Among the other names that have been mentioned as possible nominees are Karen Kornbluh, the ambassador to the Organization for Economic Cooperation and Development; and Larry Strickling, who currently heads the National Telecommunications and Information Administration, an advisory agency housed in the Commerce Department.