They really do have a problem with minorities. It's kind of hard to appeal to Latinos, women, and gays when your social policies would hurt them and their families pretty badly in a lot of cases.
They're especially hurting because they turn the poor and welfare into a bogeyman every chance they get, and there are a lot of minorities that are poor, and there are even more single mothers out there.
Yes, the GOP has a minority problem, of their own doing. They spew hatred against gays, against immigrants who are willing to work and who are educated, and the policies they push in regard to women are downright misogynistic. They have created an atmosphere whereby the poor are seen as the downfall of this country and the reason for all its ills.
The GOP has a very big minority problem, because they have a racism problem. A huge number of Republicans, including prominent Republican leaders, are very racist and very outspoken about their racist beliefs. The GOP will not be able to connect with minority voters as long as they continue to support racist policies and politicians.
In the last election the Republican Party lost by significant amounts among minorities and minority communities. It is obvious they have trouble reaching out and connecting with minorities. This is due to the fact that GOP policies and stances are often directly in opposition to equality and fairness for minorities. In order to reach out, they need to rethink their old-fashioned, racist platform.