Pre-Obama, the GOP still didn't like Putin. But when Obama was in office, the GOP was willing to look favorably on anyone who opposed Obama. And that included Putin. FOX News slowly started incorporating commentary in how Obama should be a strong leader like Putin rather than a big puss, especially when it came to handling terrorists. Granted, anytime Obama took a firm stance or stood up to the GOP, they whined about him being a fascist or using his executive powers unconstitutionally.
So they didn't ever want a fascist, but they wanted the opposite of whatever Obama did. Obama conflicted with Putin? The GOP wanted a leader more like Putin or to work with Putin. Obama negotiated with Iran? The GOP hated Iran and wanted a leader that would punish/subdue them.
The GOP is an absolute mess right now to be honest. They really have no solid political platform... the majority of their voters can only really agree upon not liking Obamacare and being tougher on illegal immigrants. That's it. The Dems are also in shambles, having lost Congress and the White House while being exposed in its campaign/election cycle corruption.
But no one is really talking about how both parties are in bad shape because everyone is fixated on Trump.