How do you create a nationwide contest to attract brand visibility?
Know that major brands are testing the waters in many online spaces, but you need to quantify how your brand (and your contest) would work for them and, more important, how your contest would be relevant to their target audiences.
In other words you have to be able to answer these questions:
Depending on the kind of campaign and the particular decision-maker you end up talking to, the sponsor also may require a complete overview of your business, your services, products, annual sales, unique site visitors per month, ongoing marketing initiatives and demographic data about your target markets and buyers.
Of course, with the internet you can create a global contest if you want (though I'd recommend getting the advice of a lawyer before you embark on any contests of any kind. There's probably some fine print you need to post to cover yourself from certain liabilities).
Getting the word out is a snap through Web 2.0 social communities, free PR portals, blogging, etc., though it's best to be strategic about how you use any promotional platforms, so you get the buzz (and meet the business objectives) you are seeking.
Best of luck with your endeavor!