"dank" means humid. Humid air considerably slows down the evaporation of the oils in the paint, so rainy weather will retard the process some. It will definitely dry after awhile, a few days at the most. The dryer the air around it is and the more circulated dry air (and heat) it gets, the faster it will dry. In other words, it would dry more slowly inside a shut closet than it would sitting out in a large open space where the air circulates better.

Don't mess around with trying to remove the tacky paint. Just wait for it to dry.