No question they do...but I have followed politics for a long time and I can't see that story having "legs"...there's no "there there". Especially once they find out the President has the right to declassify that information.
The story may not have legs. There may be no "there there." However, the average person who does not do any in depth news reading has hear it on the nightly news and now, in their mind, it's the truth. It doesn't make a hill of beans difference if it proves to be false. Remember the adage "you never get a second chance to make a first impression." In these cases you never get a second chance to get the truth out there because the people spreading the lies never take the time to correct themselves. Do you think someone like Bob Scheiffer is going to say "ladies and gentlemen, the President did not do such and such. We were incorrect." Don't hold your breath.