If the Republicans argue NBC, they will lose. She was born in Oakland. End of story. Most likely, even with Justice Kavanaugh on the Court (he'll go with the literal meaning of the 14th), birtherirism bites the dust.
All Trump needs to do in 2020 is to point out that the US needs a second term of Trump, not a third term of Obama! The electorate will agree, even enough of the minorities, to guarantee Trump a second term.