The nature of Kerrey's Bronze Star wasn't really revealed IOTL until '98-'99, when his political career was winding down (save for his 2012 failed run). If the stories break while he is still POTUS, the reactions will likely be very different, probably international news.
Agreed, I think it would be a major, major international story. And in my opinion if it broke in 98-99 I would think it would add strength to the Green Party movement in the 2000 election. Many liberals are already dismayed over Kerrey's foreign policy and this would just add fuel to the fire. I don't predict Nader to get much more support than in OTL, but I do predict he will crack 5% and throw the 2000 election into turmoil (much like he did in OTL).