What is way worse, is Obama's numbers look way better than they would have been, had millions not given up hope finding work, and therefore quit looking. That did not happen under Reagan.
There are many reasons for labor force participation rate changes. You can't just look at the number and blame it on the Presidency. Like I said, systemically Obama's recession was probably worse given the state of the financial system and Fed rates that were already relatively low. He is also President during a time when automation is more and more a substitute for lower level labor and where global competition is greater. A lot of capital that may have added jobs in Reagan's days may be adding computers or machines today. And that is no fault of Obama's, the Democrats, Republicans, or anyone else.
Then there is the whole issue of the Federal Reserve- the side that many political discussions seem to leave out for whatever reason. Amongst macroeconomists, the effectiveness of fiscal policy vs. monetary policy in spurring a recovery is still highly contentious. I think Volcker and Bernanke both did great jobs doing what they had to do in their tenures, by the way. I preferred some of Reagan's fiscal measures to Obama's too (not a fan of the stimulus as it was done- would've preferred tax cuts), but they presided over different times. Overall, it could be a lot, lot worse (imagine one of the Tea Party folks trying to slash spending across the board right now or in the last few years and actually having enough power to do so).