(CNN) Officials from the Federal Communications Commission and the Federal Trade Commission have expressed serious concerns about a draft Trump administration executive order seeking to regulate tech giants such as Facebook ( FB ) and Twitter ( TWTR ), according to several people familiar with the matter.

In a closed-door meeting last month, officials from the two agencies met to discuss the matter with a US Commerce Department office that advises the White House on telecommunications, the people said.

A key issue raised in the meeting was the possibility the Trump administration's plan may be unconstitutional, one of the people said. The draft order — a summary of which CNN obtained this month — proposes to put the FCC and FTC in charge of overseeing claims of partisan censorship on social media. But critics of the idea , including some legislators and policy analysts in the tech community, say it amounts to appointing a government "speech police" in violation of the First Amendment.

"This executive order would be the most transformative action related to the purpose of the FCC since the Telecommunications Act of 1996," said Blair Levin, a former FCC chief of staff during the Clinton administration. "This would give the FCC more power over content than it's ever had."

Agency officials now appear to share the critics' reservations. The pushback points to a sea of bureaucratic and legal difficulties ahead as the Trump administration seeks to put additional pressure on Silicon Valley's most dominant players.

President Donald Trump has been willing to plow ahead with policy before, over the professional opinions of other government experts. Beginning in 2017, for example, Trump sought repeatedly to ban transgender Americans from serving in the military, a move that multiple courts said was not supported by the Defense Department's own conclusions.

Right-wing critics, including Trump, have long claimed that an anti-conservative bias is baked into the tech industry's most popular products — though researchers have consistently failed to unearth systemic evidence of partisan discrimination.

That hasn't stopped conservative policymakers from targeting the purported effects of Silicon Valley's liberal bent. Within the White House, the people said, the efforts to draft the executive order are being led by a labor economics expert, James Sherk. Sherk spent over a decade at the right-leaning Heritage Foundation as a research analyst before joining the White House as a domestic policy adviser.

A White House spokesperson declined to make Sherk available for an interview and declined to comment on the interagency meeting. But the spokesperson referred CNN Business to Trump's previous promises to explore all policy options to address complaints of social media bias. The FCC and FTC also declined to comment.

As the Trump administration continues to work on the draft order, experts say its dubious constitutionality is just the tip of the legal iceberg.

For one thing, the FCC and FTC do not answer to the White House. As independent federal agencies, they report to Congress and cannot be ordered by the president to do anything.

The draft order addresses that hurdle, said three people familiar with the matter, by directing the Commerce Department's telecom office — the National Telecommunications and Information Administration — to ask the agencies to step in. NTIA didn't immediately respond to a request for comment.

But other aspects of the draft have raised questions, as well.

Comcast CMCSA Verizon VZ For years, under both Republican and Democratic leaders, the FCC has backed away from regulating websites or Internet companies — opting instead to regulate the providers of Internet access, such asor

In 2017, as he prepared to repeal the government's net neutrality rules for those providers, Chairman Ajit Pai praised that hands-off approach.

"The Internet is the greatest free-market innovation in history," Pai said in a speech . "Its success is due in part to regulatory restraint."

For the FCC now to assume a role overseeing social media would directly undercut that message, analysts say.

"It would completely contradict everything that the FCC said in the 'Restoring Internet Freedom Order' (RIFO) repealing net neutrality," wrote Harold Feld, a senior vice president at the consumer advocacy group Public Knowledge, in a recent blog post

The stakes are higher than the simple appearance of a flip-flop. It could mean either finding the FCC has extremely broad powers to regulate the Internet itself under Section 230 of the Communications Decency Act, or it could lead to a court tossing out the FCC's net neutrality deregulation as a case of "arbitrary and capricious" rule-making, Feld added.

Meanwhile, other legal analysts say it would be unprecedented for the FTC to prosecute a company over the way it justifies content moderation.

"The FTC just doesn't sue media companies over their editorial policies," said Berin Szoka, president of the libertarian-leaning think tank TechFreedom. "Second-guessing whether a company is politically 'neutral' would mean substituting a regulator's editorial decisions for a private company's — something the First Amendment forbids."

Thus far, officials from the FCC and FTC have largely refrained from speaking publicly against the draft order. Jessica Rosenworcel, a Democratic commissioner at the FCC, appeared to express shock in response to the draft order earlier this month with a one-word tweet: " What.

But officials have periodically signaled their reluctance to become an effective moderator of political speech.

Asked last November by Republican Senator Ted Cruz how the FTC could address allegations of conservative censorship, FTC Chairman Joseph Simons said it wasn't clear the his agency "should be addressing that at all."

"Unless it's something that relates to a competition issue, or it's unfair or deceptive, then I don't think we have a role," he said at a hearing.

Meanwhile, Pai has resisted calls by Trump to revoke the broadcast licenses of TV networks based on the content they run, saying he is a believer in the First Amendment.

But Pai has separately been outspoken in his own criticism of the tech industry, claiming in his 2017 remarks that Twitter "has a viewpoint and uses that viewpoint to discriminate."

That could put Pai in a challenging position as his agency seeks to distance itself from the draft order in its current form. As with other such interagency meetings, last month's would likely have included at least one of Pai's top lawyers, along with representatives for the White House, said Levin.

"I wouldn't be surprised if this meeting was requested by the FCC," said Levin. He added: "I think the White House would have been there. But then again, this White House works differently from a lot of other White Houses."