The most excellent and learned Powerline points out:
What about the AP’s flat assurance that “[t]here is no evidence to support Trump’s claim”? If Trump said that three million illegal immigrants voted in the election, the AP is simply wrong. There is evidence to support that claim. This study by professors from Old Dominion and James Mason Universities concluded that as many as 2.8 million illegals voted in the 2008 and 2010 elections, and the illegal immigrant population has continued to grow. The study also found that:
this [illegal] participation has been large enough to change meaningful election outcomes including Electoral College votes, and Congressional elections. Non-citizen votes likely gave Senate Democrats the pivotal 60th vote needed to overcome filibusters in order to pass health care reform and other Obama administration priorities in the 111th Congress.
Here is a link to the actual study.