There are plenty of organizations which work organizing people focused on local volunteers from the community. Democratic party was aware of their potential and they built a great campaign based on them. However, what is happening with the GOP?
It is my perspective that the GOP is less organized, centrally, on this issue. There are numerous active fundraising entities (PACs, etc...) that are focusing big budget campaigns but, at the grassroots level, to me, it appears to be more localized and less organized across the scope of the party.
Two GOP strategies come to mind. First, there was the Republican appeal to white, conservative, religious evangelicals through a grassroots approach, particularly in key areas in "Bible Belt" states. Many of these individuals were chronic nonvoters, but many of them did vote in 1980 and helped to elect Reagan to his first term.
Second, at roughly the same time, Republican candidates began to run for local political offices, such as school boards, town and city councils, as well as local executive positions. Such local political offices had come to be largely ignored by both major parties. This focus on electoral politics at the local, grassroots level ultimately helped the GOP build strength and win offices at the state and national level.