During 2014, the House Energy and Commerce Committee gathered feedback from industry groups, consumer advocates, and academics on various parts of the law. And after Republicans took control of the Senate, Thune promised that the upper chamber would launch its own rewrite.
They wanted to review the Federal Communications Commission's subsidy programs for rural and poor consumers, its authority over telecom mergers, its management of the nation's airwaves, and the various regulatory perks and obligations that local broadcast TV stations have.
But then, in February, the FCC enacted its controversial net-neutrality rules.
Supporters claim that the rules are critical for ensuring that Internet users can access whatever online content they want. The rules bar Internet providers from blocking websites, selectively slowing down traffic, or creating "fast lanes" for sites that pay.
But Republicans consider the rules a government power grab that will stifle investment in broadband networks. They are especially furious that the FCC reclassified the Internet as a "telecommunications service" under Title II of the Communications Act. The move gave the FCC stronger legal authority to defend the rules, but critics claim it essentially turned the Internet into a public utility.
All this means it will be difficult for Republicans to rewrite the Communications Act without first settling the issue of how much authority the FCC has over the Internet. And the prospects for significant legislation dim as the 2016 presidential election draws closer.
Thune and Walden have been trying to get Democrats to support compromise legislation that would enforce the core of the net-neutrality rules, while also undoing the FCC's Title II classification. Most Democrats, who believe they achieved a major victory at the FCC, have so far shown little interest in the legislation.
Walden acknowledged that he doesn't "see that there's much opportunity" to pass a bipartisan net neutrality bill. President Obama and the Democrats, he said, are "clearly locked and loaded into what [FCC Chairman] Tom Wheeler has done."
Walden emphasized that there "remains an open door" on the issue. Thune said he is continuing to talk with Sen. Bill Nelson, the committee's top Democrat, and that he believes they might reach a deal in the coming weeks.
Harold Feld, the senior vice president of Public Knowledge and a net-neutrality supporter, argued that there's plenty of common ground that lawmakers could find rewriting the Communications Act. But, he said, Republicans will have to first give up their crusade against net neutrality. He accused the Republicans on the House Energy and Commerce Committee of only fueling the partisan flames by passing a bill Wednesday that would require the FCC to do more of its work in public.
"They can call net neutrality a 'bomb,' but they don't seem to be calling in the bomb squad to defuse it," he said.