I think a lot of other people were going to that part of America as well. As Cywr said, the Portuguese were more concerned with India (or any other place that might yield immediate profit; Brasil was an accident), but it sure boosts the national ego to believe that they were in America before Columbus.
However, there is no real evidence of these discoveries (apart from the vikings). Columbus did discover America, in the true sense of that word. He was the one who brought America to everyone's conscious.