Krugman lists some of the falsehoods about Obama that Mitt Romney has been using in his campaign. Attacking the president helps him if he gets nominated by the GOP to run against him, but it also helps him in his battle for the nomination. The GOP base has been taught to hate our elected president and they respond favorably to lies about him.
Krugman's main point, however, is that the media will simply repeat the lies about Obama because they have strange view about objectivity. They believe that they must tell both sides of the political story even if one of the sides is blatantly false. Fox News and other GOP media don't observe objectivity rules but they tell their base that the "main stream media" have a liberal bias and they should not be believed. In fact, the MSM bend over backwards to avoid liberal bias.
Krugman avoids making a point, however, that needs to be made. Romney's attacks on Obama are not random. He assumes that neo-liberal ideology is a strongly held value system and his comments about Obama, even though they are untrue, place him outside of that value system. It also reinforces the ideology which is essential to the GOP narrative. His second point reinforces the ideology that is often expressed as "my country, right or wrong, my country". This is the idea of "American Exceptionalism". We are superior to other countries and we need to use our military power to project our values on the rest of the world. That is why Romney lied about cuts to the military budget, and why he lied about the president being apologetic to the rest of the world. The right wing media had a field day when the president followed protocol by bowing to the Queen of England and other leaders during his visits abroad.
There is a segment of the American population that will not be dissuaded by attacking conservative ideology. On the other hand, there is a large segment that would be responsive to a new narrative.