There was plenty of time during the Obama administration to pass gun control, and it didn’t happen, so no, false equivalence.
There were only two years (2009-10) during the Obama Administration in which the Democrats held both houses of Congress. Additionally, the Republicans held 41 seats in the 111th Congress, so they had sufficient votes to block any big gun control legislation through the filibuster. There also were a few Democrats, such as Jon Tester of Montana, who would not support gun control due to in-state politics. The Obama Administration chose to focus on other issues, such as Obamacare, rather than a big gun control battle.
Note that where Democrats have achieved majorities in both houses of the legislature and hold the governor's office, gun control measures are passed, as evidenced in Michigan and Washington state.