My short answer: no.
George E. Condon, Jr. asks this question, and provides some history. Unfortunately he picks only three examples. He probably should have mentioned Truman, Eisenhower, and Johnson, and spent more time on Reagan. In point of fact, every President who’s served a second term ever since the Constitution was amended to limit Presidents to two terms has had a lousy second term. I don’t believe this is coincidental.
As one who no longer believes that the Constitution’s Articles I-VI are fundamentally sound–I honestly believe we need to redesign its structure from the ground up–I nevertheless believe we will have this Constitution for a while. And by the nature of the current Constitutional design, it’s virtually impossible for a President in a second term to have as much influence domestically during his first term. Why? Because the American political system, by design (not intent, but by its fundamental structure, as an unintended consequence) runs on fear of The Other more than anything else. And politically, there is very little reason for anyone in Congress to fear a 2nd term President. Why? Because you know he’s not going to be running again, and is thus going to be thinking primarily of his legacy, not about helping you stay in office. Thus members of his own party no longer have as much reason to stay loyal to him, while members of the other party of course are not loyal at all, but will be turning their attention to the next elections instead.
Thus Obama has maybe 1 year to get much else done domestically, and everything else will be shoring up whatever gains he’s made and turning to the area where Presidents always have had the most power: foreign policy. Because his influence on domestic politics is weak, foreign affairs is where he can have the most influence, and most likely is where he will try.
Perhaps Obama will break the mold. I think it would require him to get deeply involved in a big public way in the midterms, which he (as other 2nd term Presidents) would be reluctant to do because if he failed it would only exacerbate his lame duck status in the final two years.
No, everything points to a 2nd term of frustrations and treading water. One thing that would fix that would be to abolish the amendment limiting Presidents to two terms, which is probably not a good idea for other reasons. Another would be to amend the Constitution again, this time allowing a President to run for another term after taking at least one term out of office (that is, you can server 8 years, then must take at least one break, then you can run again). But that too has its pitfalls.
I’m cynical because I believe the Presidency itself is an antiquated office, and a dangerous one. Nevertheless so long as we have Presidents with this much power, I doubt any President will ever have a truly great 2nd term unless they get very lucky. The basic structure of the Constitution makes this nearly impossible.