The Democratic Congressional Campaign Committee is circulating an email urging recipients to sign a petition for “A Constitutional amendment to overturn Citizens United.” To do this, such an amendment would require a rewrite of the First Amendment, upon which the court decision was based.
The Citizens United v. FEC Supreme Court case in 2010 tossed out restrictions on “independent expenditures” by corporations and unions during political campaigns. These restrictions were codified in the Bipartisan Campaign Reform Act (also know as “McCain-Feingold”) in 2002.
In the majority opinion, Justice Anthony Kennedy wrote:
“If the First Amendment has any force, it prohibits Congress from fining or jailing citizens, or associations of citizens, for simply engaging in political speech."
In response to the ruling, some liberal members of Congress introduced Constitutional Amendments to “overturn” the ruling’s consequences. Rep. James McGovern (D-MA) and Sen. Bernie Sanders (I-VT) introduced concurrent measures into their respective bodies in late 2011. The First Amendment is not explicitly mentioned in either measure, but the text does clearly identify "speech" and a redefinition of what it constitutes.
The U.S. Senate is planning a vote this month on a more recent proposal to limit free speech by amending the Constitution. Last week, Sen. Ted Cruz (R-TX) warned of just such an initiative by the Senate.