Your free speech is limited to ink and paper

Opinion Journal takes note in "Rewriting the First Amendment" that jerkweed Senators Chuck Schumer and Tom Udall are trying to do an end run around the Citizens United decision by limiting campaign contributions.  But they'll make an exception for the media:

Mr. Udall's amendment is careful to specify that nothing "should be construed to grant Congress the power to abridge the freedom of the press." In case you don't follow campaign finance, that is supposed to protect newspapers and TV networks, most of which embrace Democratic causes and candidates.

How nice of them to let the NY Times keep their freedoms.

The real target will be the corporations Democrats have railed against since Citizens United. But why should Warren Buffett's company enjoy free speech rights because he owns a handful of newspapers along with insurance companies, while Jeffrey Immelt's is muzzled because GE makes jet turbines? For that matter, what's to stop political groups from incorporating themselves as newspapers?
Once you've opened the First Amendment for revision by politicians, and reinterpretation by judges, anything can happen. We know liberal editors tend to lose their bearings when they write about money in politics, but is the problem so great that it's worth letting, say, Senator Ted Cruz determine whether the New York Times Co. qualifies for protection under the First Amendment?

I fail to see the distinction between limiting spending on speech via political contributions, clearly designed to advance a certain viewpoint, and spending on the press which is also advancing political speech.  Can the government limit the amount of money that the NY Times spends on paper?  And if there is a difference, what's to prevent the Koch brothers from purchasing every major newspaper in America?

I wonder how committed the Liberal Left would be to a "free press" if Democrats made up only 7% of journalists.