Republicans and Democrats are bracing for a busy June of primary fights that will go a long way toward determining how competitive the race for the House majority will be this fall. While Democrats face a steep hill to win back control of the lower chamber - they'd need to net 30 seats - party leaders see a chance if Donald Trump Rubio has gone from savior to sellout New culture wars erupt in the House June primary fights set stage for Dems' hopes to take over House MORE And a handful of contests this month will be some of the first chances for Democrats to select the strongest challengers in toss-up or Democratic-leaning congressional districts held by Republicans.