I think you would be able to recharacterize your contribution up until you file taxes for 2015. It's been a while since I looked at the income limit, but $193k sounds awfully close to the point where Roth contributions are limited as well.
However, since Roth is OK with you, you can probably do a backdoor Roth contribution. That is a non-deductible tIRA contribution, which you later (days or whatever) Roth convert. With a non-deductible tIRA contribution you only pay tax on whatever growth the tIRA had before the Roth conversion, not on your original contribution amount. And this gets around the income limits.
I think that would work pretty well in your case. You make the tIRA contribution any time, wait until tax time to see if it is deductible or not. If it's not deductible, Roth convert it. If it is deductible you can leave it as is.
The one gotcha with backdoor Roth conversions is that all tIRA's of the person that Roth converts (your spouse only, not you) are counted when determining the cost basis of the conversion. So if your DW has any tIRA funds for which you have taken a deduction, then you will have to pay some taxes when you Roth convert. Doesn't sound like that would apply this time if you are just opening a tIRA, but it might next year if this year's contribution is deductible and next year's turns out non-deductible. No disaster in that case, but you might end up paying taxes on roughly half the Roth conversion amount (the proportion of pre-tax to post-tax funds in all DW's tIRA's).