Partisans on both sides are convinced that their opposite numbers are constantly talking "malarkey" (as Joe Biden puts it).
Many on the right are certain that Obama is the most dishonest president ever. "Obama Lies," a rather well-documented blog, catalogues the president's misleading statements under the banner "Liar in Chief." Conservatives everywhere are sure the POTUS lied about Benghazi, and "Obama lied, people died" is a go-to headline phrase for right-leaning op-eds.
When Bush was president, the left continually accused him of "appalling lies" - most notably over WMDs in Iraq.
Meanwhile Romney's presidential campaign became a byword for lying among the liberal-to-mainstream media. Romney lied 917 times during the campaign according to Steve Benen's series "Chronicling Mitt's Mendacity." NYU Prof. Jay Rosen simply called Romney's a "post-truth campaign."
"Lying" is to some extent in the eye of the beholder, since if you like a politician you're often willing to overlook a misleading remark as a mere mistatement or gaffe. And that makes it probably impossible to estimate Republican and Democratic rates of lying with any mathematical precision.