I wasn't going to comment on the supposed scheme for President Trump to adjourn Congress and then appoint his cabinet through the recess appointment power (Article II, Section 2), on the ground that it was too fanciful and a bluff at most. But serious people seem to be taking it semi-seriously, so I took another look at it, and have these thoughts.
As my co-bloggers have pointed out (here and here), the scheme would be a complete constitutional non-starter under the Constitution's original meaning, had the Supreme Court not taken a inexcusable wrong turn in the Noel Canning case regarding the scope of the recess appointments power. But as Ed Whelan points out at Bench Memos, there's no need to even reach that issue, because the President does not have the power to adjourn the Senate that the scheme contemplates. I did not fully understand this argument at first glance, but on closer reflection I think Ed is absolutely right. Close attention to the text really does provide a definitive answer.
The first question is: where does the President get power to adjourn Congress? The answer is Article II, Section 3:
he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper.
I'll assume the adjournment power granted here applies to all sessions of Congress, not just to extraordinary sessions provided by the first part of the clause (though there's a plausible argument to other way). So the President's power to adjourn arises from a disagreement between the House and Senate as to the time of adjournment.
The second question is, how would such a disagreement arise? The answer is: Article I, Section 5. Generally, by Article I, Section 5, "[e]ach House may determine the Rules of its Proceedings", including presumably with respect to adjournment. But Article I, Section 5 further provides:
Neither House, during the Session of Congress, shall, without the Consent of the other, adjourn for more than three days, nor to any other Place than that in which the two Houses shall be sitting.
So a disagreement arises when one House wants to adjourn for more than three days and the other doesn't want it to. In that situation, the President, under Article II, Section 3, resolves the dispute. This makes sense -- if one House tries to force the other to stay in session, the House that wants to adjourn can appeal to the President to intervene.
Applied to the present proposal, however, it's clear that the Constitution doesn't mean what the proponents of the recess appointments scheme think it means. The House of Representatives doesn't have any power to demand that the Senate adjourn (a decision governed by the Senate's internal rules under Article I, Section 5). The House's power is only to decide whether to adjourn itself. If it decides to adjourn, then it must ask the Senate for consent. If the Senate refuses consent, then there is a disagreement, which invokes the President's adjournment power. If the Senate agrees to the House's adjournment, there is no dispute, and the House adjourns. But the Senate stays in session. Because there's no dispute, there's no presidential power to adjourn. The key to the whole structure is that one House can adjourn while the other does not. There's no requirement that both Houses either be in recess or be in session at the same time.
So, in an attempt to carry out the recess appointments scheme, the House can vote to adjourn. It then asks the Senate for consent under Article I, Section 5. The Senate agrees, and the House is adjourned. The Senate remains in session. There is no recess of the Senate, and so no opportunity for recess appointments (and no way for the President to force the Senate to adjourn).
Sadly, the Supreme Court doesn't get a chance to revisit its error in Noel Canning. The Senate can protect itself, without Court intervention. But, on a happier note, the President doesn't get to end-run the Constitution's requirement that the Senate consent to appointments.
Mike Rappaport adds: I agree with Mike Ramsey about the constitutional analysis. But suppose that the House claims that the Senate cannot stay in session without the House's consent and Trump agrees with the analysis, stating that the Senate must adjourn for two weeks. The Senate purports to be in session but Trump claims it is not legally in session. Trump then makes a recess appointment. The appointment is then challenged and the courts decide, presumably against the Recess Appointment.
And perhaps the Supreme Court does not accept cert. But perhaps it does. And then instead of going immediately to this issue, they revisit the interpretation in Noel Canning, overturning that case. And then maybe as an alternative ground they hold that there was no recess.
Absurdly unlikely, sure. But I can dream. But the reason to bring it up is to point out yet another absurdity about Noel Canning. It did not have to reach the "happen" and "intrasession" issues in that case, since it held the recess appointment was invalid because the pro forma session was a real session. It decided those other two issues even though they were unnecessary to the result. So why not have the Court reach those two issues again in this hypothetical case?