And whereas FDR had 14 more years of effective governing, Obama was stuck dealing the quagmires of the first two years.
It's kind of a thought experiment... had Obama been more politically astute and more politically acculturated, could he have been even more transformational?
Respectfully, I question this characterization of events. The strategy from Republicans to unconditionally oppose Obama was on the books before any policy proposals emerged. As Wallet said, as soon as the GOP gets control, everything shuts down. It hardly matters what Obama proposes; short of tax cuts, defense spending, or a sudden conversion to the pro-life camp, they were all set to propose the next thing that came out of his mouth (and even in those cases I have my doubts).
But could he have handled his first two years better with more experience? Almost certainly. ACA negotiations in the House *within* the Democratic caucus were contentious, he could've helped more there. And the same is certainly true of other major legislation like the stimulus.
Could a more effective-looking Democratic-controlled Congress have avoided losing the chamber in 2010 (and possibly hold it in subsequent elections)? It's possible. A backlash was to be expected, and to a significant extent a matter of perception rather than truth. But there's a school of thought that election outcomes are strongly tied to the appearance of effectiveness rather than the ideology or intent of the legislation approved. So if something passes "weakly" like the ACA, it looks weak and confusing to voters, whereas a big inexplicable tax cut rammed through Congress at midnight with no time for politicians to waffle on it looks strong. (I guess we'll test the truth of this hypothesis in November.)
If it turns out it's true that Obama with more experience does a better job of greasing the legislative wheels, and a "smoother" legislative process looks strong and worthy to some voters, you could lessen the Republican gains in 2010 to allow the Democrats to keep the chamber. (If a more experienced Obama avoided one or more of his biggest campaign gaffs and did marginally better in 2008, winning a handful more converts and swinging the closest few House seats into the D column, all the more likely.)
Obama without any major defeats by 2012 could REALLY reduce Republican enthusiasm for that election. With lower R turnout, we could see a more significant bounceback for the Dems in the House.
By this point it's hard to imagine what exactly the Republicans look like. On the one hand, the notion of returning to "regular order" (eyeroll) would be very strong, especially in the Senate. On the other, a movement like the Tea Party isn't just going to go away because the leaders it never fully trusted anyway haven't made any progress on their agenda. Four years is both an eternity and not very long at all in politics. I think some sort of deal might be worked out to make one more attempt for retaking Congress in 2014, and I would say they have a great chance for at least a small victory.
If they fail, god, who knows? I'm always quick to suggest schism because I think it's fun, but there's little historical evidence to suggest that's likely to happen. (But then, as is the constant reminder these days of we who work in Washington Town, stranger things have happened.)
BUT, all of that is conditional on the Democrats not losing the chamber in 2010. If a more experienced Obama only ends up helping on the margins, the OTL quagmire breeds anyway.