So reports a new Pew Research poll; the view that "The U.S. government should take steps to restrict FALSE information online, even if it limits people from freely publishing or accessing information" polled at 37%-60% (i.e., mostly against) with Republicans, and 40%-57% with Democrats in 2018 (no statistically significant difference there), but now Republicans are 39%-59% against and Democrats are 70%-28% for. Unsurprising, it seems to me: People's views on the question likely depends on how much you trust the U.S. government's judgment of what is "false information," and Democrats today trust it more than do Republicans.
To be sure, the poll question is potentially ambiguous: For instance, if one views "U.S. government" as including state and federal courts, and focuses on libel law as a kind of restriction on false information, one might say yes to the question just because one supports some sort of libel liability. But in practice, I expect that most respondents did focus on broader attempts by the Administration or by Congress to restrict supposedly false information.
Note that the debate in the U.S. about federal government power to restrict false information—including false information that is seen as harmful because it wrongly undermines confidence in the government—is almost as old as the U.S. itself, which dates back to the debates about the Sedition Act of 1798 and similar speech restrictions. The Sedition Act, for instance, banned