It's easy, if you're willing to use the internet as a by-pass medium to get around the funders that control both parties.
All other things being the same, there are five issues you can emphasize that will get you enough of the independent and Democrat crossover vote to win in the General Elections in 2008, and enough Indies and Libertarians in the Primaries.
I say this, because I am telling you what it would take to get even a leftist like me to vote for you ahead of a Democrat. In fact, I'd register as a Republican to vote for you in the primaries.
Since the cowardice of Democrats has already taken most other issues off the table, these five issues will draw voters to you and knock the crap out of the Democratic Party bosses.
1) Claim the pro-choice position. What you lose in right-wing theocrats, you will gain twofold from everyone else, especially when you adopt these other four positions. Other Republicans have done this. Pro-choice is a majority position, and the main issue that keeps many women wedded to the Democrat Party which takes them for granted on virtually everything else. Do this, and avoid sexist language in the campaign, and you'll shine like a new pair of Coroframs.
2) Call for the decriminalization of drugs, including mandatory minimums, as a violation of the most basic libertarian principles. These drug laws have been used to conduct more attacks on Black and Brown people than any weapon available to the government, and you will get massive crossover from the African American and Latin@ Democrats, as well as support from the millions -- like me -- who believe marijuana is less harmful than alcohol, and from very active white middle-class Libertarians. There are probably 10 million voters out there right now that would vote you in on the marijuana issue alone.
3) Call for an end to all corporate welfare, beginning with no-bid contracts for the Department of Defense, following with subsidies to Agribusiness, then working downward. This position alone will win support from fully 75% of the population that is tired of seeing money passed from their pockets into corporate coffers. The research on this is massive, and you could make infuriating campaign speeches every day for the next 100 years on all the legal criminality that goes on with government funding of corporations, including building their infrastructure, paying for the R&D, and passing out sweetheart contracts.
4) Call for the abandonment of all so-called free-trade agreements, beginning with NAFTA. People hate these things, and they are largely responsible (along with agri-biz subsidies) for the "immigration problems" that have everyone so het up. There is a reason that the wave of immigration began with NAFTA. It killed indigenous agriculture south of the border.
5) Call for an immediate, complete, and unilateral withdrawal from Iraq... regardless of the demagogic appeal you may employ to get the right to vote your way. If you call for this clear Out Now position, you will win masses of Independents, and more than half the Democratic Party overnight.
These are positions that could fit with a "maverick" Republican, be embraced by the more libertarian-leaning who vote Republican on the grounds of fiscal conservatism, and completely turn the left flank of the Democratic Party. I say this as someone who stumped for voting a straight Democratic ticket in the last national election.
Sure, you'll piss off some of the Republican bosses, but you'll get into Congress and then you can work your way into becoming the next Republican bosses. Run candidates who are squeaky clean, because these positions will agitate a lot of hostility from people like Boeing, Archer Daniels Midland, and Bob Jones University... but fukem, I say.
A well-run internet and canvass operation in a district of 50-100,000 people could blow away a conventional big-money campaign if you started early. Do these, and I'll go pray in public schools with you.
Good luck, and good hunting.