It was the Washington Times. I think the reporter was Dean Johnson confirming on twitter. I may not have the correct name.
https://twitter.com/Drews_Views?ref_src=twsrc%5Etfw
Drew Johnson, columnist for the Washington Times
http://theconservativetreehouse.com/2016/03/24/the-national-enquirer-runs-story-of-multiple-ted-cruz-affairs/
This seems to have the most current updates.