Perhaps read the hyphenated adjective "big-moneyed" that precedes the term special-interest in my comment. The NRA, Planned Parenthood and the AFL-CIO all make 10's of millions of dollars in direct campaign contributions[1][2][3].
This is not at all the same as what the framers had in mind with the right to “petition the government for redress of grievances” in the First Amendment. Big-moneyed special interest and influence was specifically something that James Madison was concerned about. I recommend reading "The Federalist Papers."
