That aside I don't know where you get the idea that the Republican party would be for a universal basic income. Their current position (under Trump at least) is to abolish the minimum wage in order to encourage everyone to work. And they have always favoured individual responsibility and opposed government handouts.
http://www.alternet.org/economy/how-richard-nixon-almost-gav...
Why didn't it happen, in the words of Canadian Professor Eveyln Forget (of the University of Manitoba, Canada) “The political right is afraid people will stop working and the left doesn't trust them to make their own choices.”
Also, I'm pretty sure that Trump's and probably most Republicans' position on the minimum wage is that it's ideally set by the individual states in accordance with the realities of their economies. A $15 federal minimum wage would devastate vast swaths of America by effectively banning work. The economy in much of America simply can't sustain that.
But yes, if we adopted a UBI we should most certainly eliminate the minimum wage, since it accomplishes the same goal much more comprehensively (i.e. for everyone as opposed to just those who have a job).