Can the IRS come after me forever?

No.  The IRS has a statute of limitations or CSED (literally, Collection Statute Expiration Date), which is 10 years.  There are a myriad of exceptions and tolling events that keep the CSED from running against them, however.  The most important of these tolling events are: failure to file your return (the CSED never starts to run until you file); being outside the U.S. for six continual months or more; and the time you are in bankruptcy, plus 90 days.