Why does this matter? Because a president’s credibility matters. President Bush’s second term effectively ended when Americans grew tired of his administration’s spinning and dissembling over Iraq and Katrina. They stopped trusting him. They stopped listening to him. He no longer had the moral authority to lead.
That's Ron Fournier on Benghazi and the IRS story, and it's dead wrong.
What hurt, and then destroyed, Bush's approval ratings was very simple: events. There was no way to spin the ongoing policy disaster in Iraq from summer 2003 through, well, pretty much the end of the Bush Administration. There was no way to spin the drowning of a major US city (including the parts of that which were mostly unfair to the administration). There was no way to spin a recession from the end of 2007 on, or the financial disaster in fall 2008.
Generally, if we follow Neustadt, it's better to think of these "credibility gap" arguments has applying mainly to Washingtonians -- people who directly or indirectly deal with the president -- rather than to mass publics. Voters, as such, don't pay close attention to whether the president is trustworthy, at least not as a separate category from whether they think much of him, which in turn is probably not really a separate category from (1) partisanship and (2) events.
That's easy to see in the presidency of Bill Clinton, right? Clinton certainly lied, and was caught lying, with regard to the Lewinsky scandal. But his popularity went up during that period. Why? Surely not because of his "moral authority to lead!" No, it was because of every president's best friends, peace and prosperity.
Now, obviously, it is possible for scandals to affect presidential popularity -- see Watergate in 1973-1974 and Iran-Contra in 1986-1987. But even then, my guess is that what the presidents did mattered as much as anything -- and of course, with Watergate, the lies were much larger and more consistent than anything that's even been hinted at so far with Obama.
I do think that presidential credibility matters in Washington. By the end of his presidency, neither Democrats nor Republicans really trusted George W. Bush very much, and that mattered -- see, for example, Republican resistance to TARP, among other things. But I think it's the wrong way to think about voter views of the president.