From legal briefs to pithy one-liners, the public is having its say on the proposed rules that guide how digital bits flow across the Internet.

As of Tuesday, there were about 780,000 comments, far more than for any previous rule-making proceeding before the Federal Communications Commission. The agency is fine-tuning its rules to secure an open Internet, after a federal court decision in January said it had to rethink its approach.

After the court ruling, Tom Wheeler, chairman of the FCC, proposed a path in step with the court ruling that would explicitly allow “commercially reasonable” deals. Such deals are typically for faster streaming of Internet content between broadband operators — phone and cable companies such as Verizon, AT&T and Comcast — and online media distributors such as Netflix and Google’s YouTube.

Wheeler’s plan, according to its many critics, would open the door to a two-tier Internet of fast and slow lanes, with affluent companies and households enjoying premium service and everyone else fighting traffic: a death knell for the open Internet and its democratic ethos of “net neutrality.”

Kevin Werbach, a former FCC counsel and an associate professor at the Wharton School of the University of Pennsylvania, said, “The way this has been framed for a lot of people is that the FCC is trying to change the Internet as we know it.”

Wheeler, who has been a lobbyist for the cable and telecommunications industries, has said that will not be the case, and that the agency will set a “high bar” for commercially reasonable arrangements. He has also said he is open to other ways to accommodate the court ruling.

The deadline for the first round of comments was Tuesday but has been extended to Friday. A second period for so-called reply comments will run until Sept. 10.

The court-ordered retooling of the commission’s “Open Internet Order” of 2010 has touched off a surge in lobbying efforts by two sets of big corporations — Internet companies on one side, phone and cable companies on the other.