Trump has been lying from the beginning and his supporters still elected him as President. I don't think any more lies are going to change their opinion. I'm bracing myself for eight years of Trump's lies. Unless the Democrats can organize an effective grass roots campaign, we are just going to have put up with these lies.
Not sure if this is an old question, but Trump has proven that he won't lose supporters except for the most egregious things. He did in fact lose support after the Access Hollywood tapes, but it wasn't enough to lose him the election. It just goes to show how awful a candidate Hillary was that Trump couldn't lose supporters after these fiascos.
If Donald Trump didn't lose supporters after all of the scandals and lies he has been caught in since he began his campaign, then this one lie certainly won't cause him to lose supporters. His supporters simply do not care about all of the horrible things he has said and all the lies he has told them, over and over, since his campaign began.
No, Donald Trump will not start to lose supporters. Trump's supporters do not think for themselves. All he needs to hold onto them is tell him that he will round up the Mexicans under cover of night and ship them off somewhere, or impose religious tests for admission to our country and they will do his bidding.