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.

“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.

When Obama had "Total Control" of Congress

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.

We're flying electric helicopters on Mars yet you can't turn on your clothes dryer in Texas. That's because scientists are in charge of Mars, and Republicans are in charge of Texas.