I personally do not think you can compare the Clintoon experience to now. The Clintoon episode was, in the public mind, "all about Sex" never mind that it was about the president lying under oath.
This is about the president directly lying to the American public on multiple occasions and failure to "take care that the laws are faithfully executed". Neither will play the same!
But just as Clinton was contorted to be about sex (not perjury), Obama would be contorted to be about his half-race, not about conspiring to deceive the citizenry.
Instead of a challenge to Obama's rule originating in high government offices, to be successful perhaps it would need to originate from the ground up; eg. citizens angry about the cost of their healthcare, or their family doctor being taken away, etc.
Is there a conservative community organizer in the house? Liberals are effective, because they can stay on topic.
But with only 2 years remaining, I believe the GOP would be more wise to demonstrate their ability to run things, instead of failing to unseat Obama, and losing trust.
It is not a matter of deserving to be removed from office, but instead a matter of judgment, priorities, risk assessment, etc.
IOW the GOP is now in power to show it can run things BETTER, NOT to bring Obama down.