Over at The American Conservative, a number of thinkers address the question (via bookforum). Paul Gottfried:
I have no hope for any alliance between the antiwar Right and any significant leftist force. Individual liberals may establish informal relations with self-identified conservatives, but one should avoid generalizing from this observation. Individual libertarians, like Bill Kauffman and Justin Raimondo, may get on well with maverick leftists Alexander Cockburn and Gore Vidal. But this does not foreshadow larger trends. During the Bush administration, the antiwar Right struggled to connect with leftist opponents of the war, and they received hardly any attention from their would-be partners in organizing antiwar activity.
The reasons for this non-recognition seem self-evident. First, the Left has no interest in being allied to social reactionaries by becoming identified with the antiwar Right. The Left is happier to deal with “conservatives” like David Frum and David Brooks, with whom they agree on most social issues, even if they remain apart on foreign policy. For those who consider gay marriage, unrestricted abortion, and special rights for minorities to be paramount issues, having Catholic traditionalists or paleolibertarians as allies is not a genuine strategic option.
Second, there is no recognizable advantage for the Left to be allied to marginalized people on the Right. As long as neoconservatives control the media and financial resources of the conservative movement, no one, except for hopelessly deluded antiwar rightists, would consider an alliance with our side to be a political coup. Unless the antiwar Right can push itself into public attention and counteract the neoconservative-fashioned image of “conservatives,” the Left can have no practical interest in reaching across the ideological chasm.