I think some of the loudest voices in your party, aren't welcoming. When the talk turns to immigration or welfare, many times the tone of the conversation is mildly insulting to minorities.
Also, it's going to be harder for the GOP, because public perception is that you are the party of the rich white guy, and the fact that your party IS over 90% white is a barrier.
This best thing the Obama campaign did, was use a grassroots technic in swing states, getting an army of local people out knocking on doors and talking to neighbors. This is, IMO, what the GOP needs to spend time doing, organizing local republicans, and bringing the message to people's doors.