WASHINGTON — Even before President Obama issued his forceful call this week for “the strongest possible rules” to protect an open Internet, Tom Wheeler, the chairman of the Federal Communications Commission, was in a tight spot.

His quandary: trying to shape rules for an open Internet, or net neutrality, that would satisfy the millions of people who wrote the agency in support of strong regulation — and also would stand up in court and encourage web investment and innovation.

The challenge only grew after Mr. Obama spoke out, adding a more potent political element to the debate. Since those remarks, say people who met with Mr. Wheeler this week, he has been testy, defensive and a bit angry that he might be seen as a political pawn instead of as the head of an independent agency who is exercising his own judgment.

Mr. Wheeler has not yet decided on how to proceed, F.C.C. officials say. But as he tries to thread the needle of politics and public policy to safeguard the openness of the Internet, he must now also face down angry Republicans in Congress and a technology industry, generally supportive of the president, that is wary of any regulations stifling the expansion of the Internet.