Constitutionality of White House "Czars" Questioned

Amid the fallout of the Van Jones (Obama's former green jobs adviser) resignation, many are now questioning how the White House has been relying upon "czars" to execute the Administration's agenda.

Technically just "advisers" to the President, the czar system, which has been around since Nixon, actually exploded during the George W. Bush reign. Dubya pushed legislation through Congress which grants his advisers access to confidential information formally available only to those with Senate confirmation. Since the czars work within the West Wing, they enjoy almost total immunity from any accountability to Congress under the claim of executive privilege, according to an analysis by FOX News' Andrew Napolitano.
Having unelected, unaccountable "czars" running federal agencies and doling out taxpayer dollars is clearly unconstitutional. Therefore, some Republicans are now suggesting a "shadow government" might be managing everything from health care, climate change and Afghanistan to the auto sector. GOP critics claim there could be between 30 and 44 czars in the White House. But their case obviously isn't helped by the fact that about a third of those czar positions were there during the Bush years.
Congressman Patrick McHenry wants 44 of Obama's advisers to testify before Congress to determine whether their duties are actually allowed by the Constitution. From his open letter:

If the czars have high-level, decision-making authority as their titles would indicate, then it is my concern that their appointment without Senate approval represents a circumvention of our Constitutionally-mandated confirmation process. On the other hand, if the czars have no actual power, then I am equally concerned that taxpayers are fronting the bill for the salaries of these figureheads and their staff.