The idea that social conservatism is the GOP's biggest problem is laughable, with the possible exception of immigration. By far the biggest issue is economics - broadening appeal on that league will garner far more votes than abandoning the party's most loyal voter base.
The Republican Party should regularly be winning the votes of affluent minorities and minorities with sympathy toward the business community/entrepreneurial spirit/efficient governance, but we get clobbered with those voters. Why do you think that is? Because my theory is we come across as a racist and xenophobic party. A lot.