"The Declaration of Independence" is a painting by John Trumbull from 1786. He was a Harvard educated American painter, and was also a descendant of the Pilgrim leader John Robinson. The painting depicts 48 members of the drafting committee in a room presenting the Declaration of Independence to Congress. The rug that is under the table could be of the Wilton type, which were usually created as long, narrow strips of carpet which were then stitched together. Wilton style of weaving has been around for hundreds of years and offers a variety of textures although a limited amount of color choice. Several generations later, Wilton rugs can still be found on eBay.
Although there are many historians who criticize the paintings' lack of historic accuracy, we're certainly glad a rug was included. The dispute made is based on the probability that not all people represented in the room were there at the same time for signing. Nevertheless, as seen below, the painting shows the drafting committee presenting the work to Congress before the actual signing.
Declaration of Independence by John Trumbull