CT
Identification of spiders is not my specialty. Spiders can be tricky to ID from one photo, as it is important to see the number and location of the eyes as well as the mouthparts. With that said my guess is the Funnel-Web Spiders, Family Agelenidae. This family would be easy to ID if you see it in its web since as the name suggests - it is on the ground or in foliage in the form of a funnel - very tightly webbed. But from the clothesline that could be a challenge.
Here are some images to look thru to see if you have a better idea from seeing the critter in person.
