"... by staying home and allowing the minority to gain strength." Did you mean to write 'by NOT staying home'? If not, I'm not getting it ...
"We have to make it easier for the moderate repubs to agree with the conservative viewpoint more often - not less often by staying home and allowing the minority to gain strength."
Because, if we stay home and allow the minority to get larger .. it will make it harder for the moderate repubs to side with conservative ideas because the moderates will be under more pressure from the minority. I revised the sentence a little - maybe that makes more sense to you.