"Real" Unemployment rate is whatever you measure, as long as you're consistent. We can call this "real" one U4 (currently around 6%), or the one you seem to like U6 which has dropped significantly since your reference. Both are better when Obama took office, when the nation was shedding jobs like crazy. Both are better overall even though the government has shed jobs since Obama took office (yes the government is smaller under Obama, you don't hear about that much). To get a better unemployment number, the private sector needs to grow to offset the losses in the public sector, and still some more. Obama's not doing a horrible job.
Obama did have a decent hand in lowering unemployment. It's just not enough. Even early on in the recession people told him to spend more, and he knew he couldn't get a real spending bill past Congress (and we're still at historically low interest rates on bonds, money is cheap! Build infrastructure, baby!). But, instead of saying "hey we need more, but this is all those suckers will give us" he was very "this should be enough". He never recovered from that. It truly is his mistake, and it cost him much in both sets of midterms.
There is a narrative that Democrats are lousy on the economy, when the economy tends to do better with Democratic Presidents.
As far as how many he should have added, hmm, that's a good question. Comparing to the 60's - hmmmmmm. We had a postwar dividend, in both pent up consumer demand, and baby boomers becoming new consumption targets. We didn't have globalization then. Japan and Germany were still recovering from the war. China wasn't even on the map economically. No Internet, no offshoring, no robots. It would be an interesting discussion on whether we could *ever* get back to that kind of increase. I have kids, I wish we could. But can they ever win a job from Watson?