CHARLESTON, South Carolina — Former U.S. Ambassador to the United Nations Nikki Haley rejected speculation that she would join a third-party presidential ticket with No Labels.

But even if Haley reneged and teamed up with No Labels after her path to the White House became considerably difficult after losing South Carolina’s GOP primary on Saturday to former President Donald Trump, an independent run faces legal hurdles that would severely limit a path forward to the White House.