For a list of bills that were proposed in the 113th Congress, you can follow the link below. Once at that link, you can click on sequentially numbered sets of bills to see all of the bills proposed during that Congress in either house.
If you use the site in the link below, you can find that the first bill introduced in the Senate in the 113th Congress was entitled “Immigration Reform that Works for America's Future Act.” That bill was introduced on January 22, 2013. It was cosponsored by 15 senators. Like so many bills that are introduced in Congress, this bill really did not go anywhere. It was referred to the Senate Judiciary Committee where no action was taken. You can see a synopsis of the bill, a list of its cosponsors, and other information at this link.