There isn’t very much to the GOP’s broad appeal outside of opposing new taxes. Part of their brand used to be their “strong on defense” image, but two expensive and unpopular wars have destroyed much of their advantage on that front, and turned the American people against neo-conservative thinking.
The GOP’s other draw is an appeal to conservative religious values, like opposing gay marriage and abortion. While these issues are fundamental to a large segment conservative Christians, a huge part of the country feels differently about these issues, or considers them not very important.
No, the aspect of the modern Republican brand with the broadest appeal (and basically their entire economic platform) is their commitment never to raise your taxes. Yes, people claim to care about the deficit, but people don’t feel the deficit. People do feel changes in their tax rate. It is no wonder that time and time again, when it comes to choosing between lower taxes or reducing the deficit, the Republican party chooses lower taxes. Deficit reduction is simply not as core to the Republican brand as the pledge of no new taxes. That is why you could have Dick Cheney out there saying “deficits don’t matter.”
It is true the Republicans could go after this “sacred cow” to get something they want more. But there is nothing they want more. “No new taxes” isn’t an aspect of the Republican party platform, is it now essentially their entire brand. If the Republican party supports raising taxes so a Democrat can reduce the deficit, what would be the pitch the GOP uses to win over non-religiously conservative upper middle class voters?