First to the dictionary ...

 

  twit  

    To taunt, ridicule, or tease, especially for embarrassing mistakes or faults.

    n.
    1. The act or an instance of twitting.
    2. A reproach, gibe, or taunt.
    3. Slang A foolishly annoying person.

Then, to The Twit ... (obviously, choose which meaning has most meaning for you ...)

Senator Clair McCaskill (D-MO) loves twitter. On more than one occasion and re more than one issue, Claire's Twitter comments have raised eyebrows for their "embarrassing mistakes or faults". And, on more than one occasion, people have used Twitter to twit Claire about her statements.