Accusing people of 'playing the racist card'.

Let's say, hypothetically, that a President says something overtly racist.

His opponents, especially those who are part of the attacked group, call his comments racist.

Then the President and his supporters make the following claim:

"You guys just call anyone who disagrees with you racist."

This is factually wrong, and can be shown to be so (which seems to matter less and less these days) and the original comments were objectively racist.

Is the defence just a lie, or does it conform to some specific fallacy? It is a Straw Man or is there one that fits better?

I think it is just a simple case of exaggeration or hyperbole .

I'll go w/ Dr. Bo on hyperbole. That about says it.

It's also a basic diversion. There are several logical fallacies involved there: shifting ground, red herring, etc.

It's hard to talk about issues when people get defensive, isn't it?