I don’t think there’s any government sponsored investigation going on, so any money used would be by journalists and publications. (someone correct if I’m wrong, please)
I think the biggest effect it may have on the presidency is that his lawyers are being outplayed in this case so far. By saying he didn’t sign the NDA they force him to either step forward and say it’s all true, or allow them to control the narrative now and look for compensation later. He doesn’t have control of what’s going on, and everyone else he’s dealt with is watching.
If that continues and there’s a judgement that those NDAs that he’s had wives, girlfriends, and accusers sign aren’t as enforceable as previously thought, that may be the real damage.
(for the record, I think if you take the payment on those deals, they’re assumed to be agreed upon, but I also think it’s impossible that deal was made without one of the named party’s knowledge, so we’ll see.)
I’m not saying that will happen, but that possibility is what needs to worry Trump’s team more than this single incident. 2018 is a whole different ballgame and the barriers to bringing sexual misconduct to light, even against a sitting president, are not what they were even 5 years ago.