Obama did not "own" the Senate for two years. It was actually just a few months, because of Republicans delay in seating Franken, and then Kennedy dying. Just long enough to get that herd of cats to pass a severely compromised ACA.
When Obama had "Total Control" of Congress
“Total control” of Congress by Democrats lasted all of 4 months. From September 24, 2009 through February 4, 2010...at which point Scott Brown, a Republican, was sworn in to replace Kennedy’s Massachusetts seat.
That "Two Years" is a Republican meme used to negate Democrats desire for positive changes: IE. "If Democrats really wanted X, then Obama could have passed that when he had control of congress for two years.