Stage four cancer would dictate immediate, aggressive treatment if there is any hope of survival for more than a short period, depending on where it started, and where it spread. Given that Specter seems to have declined treatment, my guess is that he probably has six months.
Specter is undergoing chemotherapy during which he'll continue working.
http://www.cnn.com/2005/ALLPOLITICS/02/16/specter.cancer/