Speaking as a one time "Democratic Socialist," I think the way to a leftist's heart is through the issue of civil liberties. I've always thought the issue of civil liberties was a huge consideration in making voting decisions. I don't think I was unusual in that respect. But it took a while, literally years of rethinking and reconsidering my perspectives, to come to the realization that liberty was incompatible with government strong-arming.
So, the pitch is something like this: Ron Paul opposes the Patriot Act. He is as alarmed as you are, and as no Democratic or other Republican candidate seems to be, about Bush's excesses of executive power, domestic spying, the suspension of habeas corpus. He wants to end the drug war. He wants to keep the federal government out of your bedroom. Much of this is in common with Green Party concerns, although they are overly fond of national government programming, but some may be persuadable.
Also, you could send them to re-education camps and make them read F.A. Hayek's The Road to Serfdom. OK, skip the camps, but recommend the book. He makes a compelling case that the kind of government planning and control they want is incompatible with the kind of liberty they want.
As has already been pointed out, many on the left simply aren't going to take kindly to Ron Paul's ambitions to dismantle the welfare and nanny state as we know it. Many just won't be persuaded. But some, I presume, may be like me - alarmed enough about the erosion of privacy and liberty to do some serious reconsidering of what kind of government they really want.