TAM is has New York and Miami on sale using Fidelidade points for travel between May 20 and June 11, 2014, that are booked between March 17-23.
You pay 18,000 points for economy one-way and 45,000 points for business class one-way. There are no fuel surcharges for trips originating from Brazil.
You can access this offer on TAM’s web site here. You may have to use incognito window, set your country to Brazil and then copy/paste the link before it opens up correctly.
TAM’s bookings for the Miami and New York routes must be soft late May/early June. I am avoiding Brazil until the World Cup frenzy is over and the prices somewhat back to normal.