Cheap Hawaii honeymoon?

Starting to think about our honeymoon... Is a 'cheap' Hawaii honeymoon even possible? Something under $3,000 all inclusive?

I'm a teacher, so we won't be able to do it until February break or April break (President's week and Easter week). Are we completely unrealistic to think we could do a honeymoon to Hawaii (our dream) or someplace else tropical for under $3k?

Please advise! thanks :)