Beyond the Freudian slip of suggesting that MasterJedi is on the Court, there are a couple of problems here:
Hilariously the Constitution may only allow for the impeachment of President, Vice President and Supreme Court Justices. I say "may" because as ever, the constitution contradicts itself in about three different places.
I base this opinion on Article I Section 3 Clause 1 which states:
"...Impeachment charges may be brought upon the President and Vice President, and Supreme Court Justices." There are however other sections of the Constitution that suggest that all "civil officers" may be impeached, though it never actually defines what a civil officer is.
I do however agree that the lack of activity on the part of a cabinet member should be an impeachable offence.
I agree with you. Everything in the constitution in regards to impeachment is a big, bloody mess. In fact, I'm not even sure if the impeachment proceedings are supposed to originate with the Chief Justice or the Senate. One of the reasons I did this was to draw attention to the constituitonal crisis. More importantly, though, I feel it is important that the members of the court and cabinet are both active and qualified to face the coming constitutional crisis.