Can New Jersey Recall Their US Senator?

From the amount of media exposure this is getting you wouldn't realize the magnitude of what is playing out in New Jersey. NJ Tea Parties United has started a campaign to recall US Senator Robert Menendez. Senator Menendez was elected in a 2006 mid-term election after being appointed by recently defeated governor Jon Corzine.
New Jersey Secretary of State Nina Mitchell Wells, whose powers are mostly clerical, has claimed the campaign is unconstitutional but under which constitution? In 1993, New Jersey amended their constitution giving the state the ability to recall local, state and federal elected officials.
This will be a great one to watch as it unfolds - not only would it be a huge blow to the Progressive party but it would give more government power back to the states.