The source for the news that Rep. Peter King will introduce legislation banning guns in proximity of members of Congress comes not from King, but from a press release from Mike Bloomberg's Mayors Against Illegal Guns. Here's what that group claimed this morning:
Congressman Peter King today also announced that he will introduce legislation that will make it illegal to knowingly carry a gun within 1,000 feet of the President, Vice President, Members of Congress or judges of the Federal Judiciary. In the United States, it is illegal to bring a gun within 1,000 feet of a school. Passing a similar law for government officials would give federal, state, and local law enforcement a better chance to intercept would-be shooters before they pull the trigger.
King has not commented further on this yet.
UPDATE: King appeared at the presser in New York and announced this; the next question, it would seem, is what Constitutional authority can be cited in the legislation.