In 1585 Columbus submitted his proposed plan to King John II of Portugal for financing. John asked the opinion of his experts, who specifically rejected it because they believed Columbus’s estimates of the distance were far too short. He tried again in 1588 and was rejected because by that time the Portuguese had rounded the Cape of Good Hope and saw their way clear to India by that route.
Columbus also sought support from Venice and Genoa, and his brother Bartholomew went to England, all without success.
Columbus proposed his plan to Ferdinand and Isabella in 1586, but it was rejected after being reviewed by experts on the grounds that the distance was too short.
However, he continued to lobby the Spanish monarchs. Ferdinand finally gave in in 1492 after the expulsion of the Moors freed up some funds. (Isabella continued to be mostly against it.) I think they figured it was a long shot but this madman might discover something out there.