There are a number of sources you can use to track immigration legislative developments. One good source that is free and easy to use is congress.gov. You can use it to find both current and archived bills and their bill tracking reports.
You can find pending federal bills on congress.gov. You can search by bill number or bill topic.
For example, you can search for bills that contain: immigration
For each bill, the site provides a bill tracking report with information about the bill, where it is in the legislative process, etc.
Example: H.R. 1614 - Destigmatizing in Immigration Act
Lexis has a neat bill passage prediction feature. If you want to figure out if a bill will pass, you can retrieve it on Lexis and then look at the Legislative Outlook. (Note: This is not all that useful for immigration bills, since everyone already knows they rarely pass.)
Example - H.R.1614 - Destigmatizing in Immigration Act
