The strip has famously pulled few punches when it has come to those in the Oval Office. I've heard of lots of criticisms that have been leveled at Garry Trudeau by various other people he has satirized over the years, I'm curious as to whether any American presidents (especially while still in office!) have had comment to offer on how they've appeared in his widely syndicated strips.
Writing not as an historian, but as someone reasonably well-versed in the history of Doonesbury up to 2005, my observation is that most political figures who were targeted by the strip simply ignored it.
It's an effective strategy because Doonesbury is far more often commentary than original reporting. Given the long lead time of a comic strip -- initially more than a month; now perhaps ten or so days -- the information Trudeau presents has usually already been dealt with. Questions have been asked, and answers given.
Thus, there is little incentive for a reporter to name-check Doonesbury when asking a question, and less incentive for a politician or their spokesperson to give a substantive reply, beyond something like:
"I would ask you to refer to our previous statement and your notes; we have already addressed the facts of this matter. As for Doonesbury and its author, well, it's no secret where Trudeau's sympathies lie."
(That "quote" is wholly of my own creation, though its content and construction may be somewhat informed by previous research I have done on this subject.)
Some exceptions are covered in [the second chapter of Chris Lamb's Drawn to Extremes] (http://books.google.com/books?id=LxCtgSAuXM0C&printsec=frontcover#v=onepage&q&f=false). It's [a rather expensive purchase] (http://cup.columbia.edu/book/978-0-231-13066-0/drawn-to-extremes), but the excerpts available on Google Books may be enough to satisfy your curiosity.
EDIT:
You will also notice that in most cases where Trudeau did draw a substantive reply from the target of his criticism he was operating somewhat ahead of his normal process, by (for example) throwing a local issue into a wider spotlight, as he did with [his series on the Palm Beach peon registration law] (http://www.gocomics.com/doonesbury/1985/06/18/), or by framing the debate in an especially novel manner, as he did with [Bush's manhood] (http://www.gocomics.com/doonesbury/1984/10/29) and the [Texas fetal sonogram bill] (http://www.gocomics.com/doonesbury/2012/03/12).
Trudeau probably wasn't the first person to imply that Bush lacked balls, or to observe that mandating an invasive fetal sonogram when not medically necessary amounted to a rape under color of law, but he certainly had the most prominent platform.