First, the problem is not right or left in the sense purely of Republican and Democrat. As discussed here repeatedly, the overwhelming majority of Republicans, with very few exceptions, are NRA stooges on gun control. A minority of Dems are also,m but it is not "left" or "right," it is primarily regional.
Second, what you are really saying here is that the Dem party could have worked to curb access to guns when it was in power. My response is that Obama did put in place limits on assault rifles, and that was lifted by the GOP. The Dems in local areas attempted some restrictions, but were stopped in the courts by the NRA.
So what you can glean from this is the following truisms: 1) As long as the GOP controls the Congress and the WH, the odds of any meaningful gun restrictions being enacted are exactly ZERO. None. Nada. Zilch. 2) If the Dems are in control, there is at least some chance for meaningful reform. It will be limited by the courts to reasonable restrictions, and there will be elements in the party that fight it for the NRA, but literally the country's only chance if it wants reform is to put Dems in control.