Washington’s zeal to rein in Big Tech could be one step closer to fruition if a proposal floated by two unlikely partners in the Senate — Elizabeth Warren and Lindsay Graham — makes any headway in the current Congress.

The two senators have proposed legislation to create a new government agency with the power to regulate big players in the technology space, such as Google, Facebook, and Amazon. The new agency would be modeled on others created to regulate specific industries over the course of the last century, like the Federal Communications Commission, the Federal Trade Commission, and the Nuclear Regulatory Commission.

The name of the legislation — the Digital Consumer Protection Commission Act — suggests what this new agency might be called.

“Nobody elected Big Tech executives to govern anything, let alone the entire digital world,” the senators said in an opinion article published in Thursday’s New York Times. “If democracy means anything, it means that leaders on both sides of the aisle must take responsibility for protecting the freedom of the American people from the ever-changing whims of these powerful companies and their unaccountable C.E.O.s.”

The liberal senator of Massachusetts and the conservative of South Carolina suggest the new agency would be charged with licensing and policing the tech giants and backstopping the regulatory efforts of other federal agencies and state attorneys general. They want to circumvent existing legislation that largely shields social media companies from liability for material shared on their platforms and require those companies to “mitigate” the risks posed by content deemed harmful to certain groups and allow people to sue those companies if they refuse to do so.

The senators say the legislation would also raise the bar for mergers and acquisitions in the technology industry and tackle what they called the industry’s anticompetitive practices. “Reining in tech giants will be hard, but it’s a fight worth fighting,” they say. “If we win, Americans finally will have the tools they need to combat many online evils harming their children and ruining lives.”

The proposal has so far gotten mixed reviews in the public sphere. Liberal Democrats and some in more populist conservative circles — particularly those who have complained loudest about technology censoring conservative viewpoints online — hailed it as long overdue and necessary to rein in a group of companies that have become too big for their own good.

“Passing the Digital Consumer Protection Commission Act is critical to preventing a few dominant internet companies from unfairly taking advantage of consumers and eroding our democratic values,” the president of the liberal Center for American Progress, Patrick Gaspard, said. “This bill will ensure that the digital playing field is no longer stacked against competitors, consumers, and the public.”

Other conservatives and their libertarian-leaning allies questioned the need for yet another federal agency to control the private sector and stifle innovation in one of America’s most robust industries. A former FTC official now at the Center for Growth and Opportunity at Utah State University, Neil Chilson, says one of the biggest dangers of creating a single-industry regulator is the inevitable regulatory capture, a term used to describe when an institution becomes dominated by the industry it was meant to tackle.

“Regulatory capture is particularly bad in fast-moving tech areas, because incumbents use it to prevent disruptive innovators,” Mr. Chilson said on Twitter Thursday. “Warren and Graham point to the FCC as a model for their bill, but the FCC perfectly shows how an industry regulator can be weaponized against competitors.”

“Thankfully the Warren/Graham bill isn’t going anywhere,” Mr. Chilson predicts. “But I’m sure it won’t be the last time this idea surfaces.”