[The President] shall nominate, and by and with the advice and consent of the Senate, shall appoint ambassadors, other public ministers and consuls, judges of the Supreme Court, and all other officers of the United States, whose appointments are not herein otherwise provided for, and which shall be established by law[.]
Could the Senate legally just decide that no more appointees would be confirmed and positions left vacant, for a long period? Are there limits on "long period?" (A more extreme version of the question is here.)
This question is, of course, motivated by current happenings and statements from the Senate Majority leader that "no Supreme Court nominee from President Obama would be considered."