John Elwood notes the possible connection between the Senate change in the cloture rules and the Noel Canning case. His focus is on the effect of a decision that invalidates the recess appointments, but I believe a strong case can be made that this action may affect both the outcome and the reasoning. Systematic filibusters of nominations for executive office provided a strong functionalist rationale for allowing the President great latitude in making recess appointments. If a minority in the Senate can disable an executive agency from functioning, there is a good living-constitutionalist case for allowing the President to do something about it.
But this functionalist rationale is substantially undermined by the elimination of the filibuster for executive nominations. Such nominations will now succeed if they glean majority support in the Senate. In the current configuration, such majority support will be routinely forthcoming.
Although there is much argument about the original meaning of the Recess Appointments Clause, my current opinion is that the original meaning would forbid both (1) intrasession recess appointments, and (2) recess appointments to vacancies that do not arise during the recess. But with the filibuster, decision of Noel Canning on either or both of those grounds would have been costly in functionalist terms--because it would have substantially reduce the President's power to circumvent the filibuster.
Without the filibuster, the pathway to an originalist decision is far more attractive. Of course, functionalist considerations might not have deterred Justice Thomas or (perhaps) Justice Scalia, but other members of the court might well have seen this as a reason to limit the decision to the third issue upon which certiorari was granted: "Whether the President's recess-appointment power may be exercised when the Senate is convening every three days in pro forma sessions."