In situations where an Amendment like that is passed, isn't the sitting president unaffected by it? I recall reading that Truman was not affected by the 22nd Amendment and could have ran as many times as he wanted. So wouldn't Reagan still be restricted to two terms and it would be his successor and after that would be eligible for a third term or more? I think if Clinton ran in 2000 he would have beaten Bush by maybe a 4 point margin in the popular vote and a comfortable Electoral College margin. Obama probably beats Trump in 2016 by a slightly bigger margin than he won by in 2012.
The sitting president (Truman) was explicitly unaffected by the passage of the 22nd amendment, from the Section 1 text:
"But this Article shall not apply to any person holding the office of President when this Article was proposed by the Congress, and shall not prevent any person who may be holding the office of President, or acting as President, during the term within which this Article becomes operative from holding the office of President or acting as President during the remainder of such term"So, a simple repeal of the 22nd amendment would allow previously term-limited presidents to run for third terms.
