Raw Story calls Burkman "powerful," based in part on The Hill's assessment that he signed more new lobbying clients in 2013 than any other firm. In fact, the firm did less than $2 million in business in this Congress, through the first three quarters of 2013.
And Burkman isn't just a lobbyist. He's also a heavy-hitter with 21 followers on Twitter, a "radio show" that appears to be nothing more than a podcast, and a pronounced issue with gay people. Here, from last February, Burkman criticizes the establishment media for forcing the Boy Scouts to accept gay people: "Ladies and gentlemen, if you have a son, if you have a son in the Boy Scouts, get him out now." As of writing, the Boy Scouts of America has not collapsed in a moral panic.
It's not clear how Congress would even enforce a ban on accepting gay players, which is one reason that policy experts, not lobbyist/podcast hosts, are generally the ones to draft legislation. The league receives some tax exemption, but that's a small stick for Congress to wave. Any attempt by the government to limit who private entities might hire would 1) probably lose in court and 2) seems somewhat contrary to the worldview of a conservative like Burkman.
Burkman says he has political support for the measure, which is probably true. But he didn't indicate to The Hill any members of Congress who might want to carry a lobbyist's anti-gay NFL bill — perhaps because there are not many members of Congress who would be willing to do so.
Update: Burkman told the Huffington Post's Sam Stein that he has five members of the House and a senator interested in co-sponsoring the bill. He didn't name any of them.
Burkman's real goal is actually to get people to talk about Jack Burkman. He has succeeded, so now we can all go back to not knowing who he is.