The most significant constitutional question in the case concerns the double layer of removal restrictions. As the DC Circuit described:   "[T]he President is two levels of for-cause removal away from Board members, a previously unheard-of restriction on and attenuation of the President's authority over executive officers."   There isn't much law in this area and for now the most applicable precedent is Morrison v. Olson, 487 U.S. 654 (1988).  Morrison involved the constitutionality of independent counsel.  Counsel was appointed by a panel of judges and could only be removed for cause by the attorney general.  

The Supreme Court upheld the removal restriction emphasizing that the independent counsel was a position with limited jurisdiction (the panel of judges assigned the relevant matter for investigation) and limited duration (it went away once the investigation was completed).  Although these were the factors emphasized by the Court, it wasn't really about limited jurisdiction or tenure.  It was about whether the task performed by independent counsel somehow involved a critical executive  function.  As the Supreme Court concluded:  "we simply do not see how the President's need to control the exercise of that discretion [the discretion exercised by the independent counsel] is so central to the function of the Executive Branch . . . "  In other words, restrictions on removal of employees in the executive branch are permissible if they are imposed on personnel who are not that important to the function of the presidency.

That accurately describes the PCAOB.  Even though the jurisdiction is arguably broader and the tenure longer (at least more definite), the task of regulating independent auditors isn't central to the function of the president. 

But even if the office can be subject to removal restrictions, that does not mean any restrictions will pass constitutional muster.  If for example Congress were to provide that removal could only occur with the advise and consent of the Senate, this would be unconstitutional, even if it applied to non-central personnel.  In Morrison, the Supreme Court concluded that Congress could limit removal of non-central personnel to good cause where the cause was exercised by the Attorney General.  Presumably, had Congress instead prohibited removal by the president (or anyone appointed by the president), this would have been unconstitutional.  The president must have at least some residual right to police the actions of the members of his or her branch, particularly where they engage in misconduct.

The issue in the PCAOB case, therefore, is whether the double removal restriction was so severe as to deprive the president of any ability to supervise employees in his/her own branch.  One could imagine, for example, that a quadruple removal restriction (four layers of for cause removal restrictions) would make the president's authority to remove so attenuated as to deny it completely.  That was the question in this case:  Whether the president's ability to remove was so attenuated, it effectively did not exist.  Moreover, the analysis might change somewhat depending upon the importance of the non-central official at issue.

In this case, though, the answer is no.  The SEC has extensive supervisory authority over the PCAOB.  The authority constrains the actions of the PCAOB, limiting its discretion.  This oversight is a form of presidential supervision since the commissioners on the SEC are appointed by the president.  Moreover, if real misconduct occurred and the SEC did nothing, the president likely could remove SEC commissioners (for cause) and appoint those who would take the necessary steps against the PCAOB.  Its a blunt authority to say the least.  The president won't be likely to remove members of the Commisson for failing to act against the PCAOB except in the most extreme circumstances.  But that's the point.  In the most extreme circumstances, the president could intervene.  Short of that, the structure requires that auditing standards  be kept above the political fray.