In the senate the democrats did have their 60-40 advantage from 7 Jul 2009-25 Aug 2009 and then a 59-39 advantage through 9 Sep 2009, then back to a 60-40 advantage 25 Sep 2009-4 Feb 2010 then a 59-41 advantage until Nov 2010. If I read that graph right.
In the house the Democrats held a 256-178 advantage with each party gaining and losing a seat now and then throughout that 2 year period.https://en.wikipedia.org/wiki/111th_United_States_Congress
Anyway you look at it, the democrats controlled both the house and the senate for Obama's first two years. Although not two years of filibuster proof senate, regardless they still controlled the senate and the house along with the presidency.
Now what does total control mean? The Democrats had total control of government for the entire two year period, the presidency, the senate, the house. Does total control mean filibuster proof senate also? Do the Democrats have total control of the government today? They have the presidency, the house and the senate. Granted the house is 222-213 and the Senate a 50-50 tie with VP Harris the tie breaker.
Regardless, even today the Democrats control the agenda and make up the rules for each chamber to operate under.
Yeah, I remember republicans saying that, asking why didn't Obama and company pass this or that when they controlled both chambers of congress and the presidency. Immigration reform was a big one. I think the reason why is the democrats put health care as their number one priority and not immigration reform. Which in my opinion the Democrats decided to tackle the toughest to get passed first, healthcare while all other things waited.
Election wise, that was a huge mistake. Although the ACA is fairly popular today, it wasn't through Obama's entire presidency.https://www.realclearpolitics.com/epolls/other/obama_and_democrats_health_care_plan-1130.html
It took Trump to make the ACA popular.