They would if Trump himself made it an issue. He would have the standing to challenge Harris' eligibility. All he needs is to get a friendly judge in a friendly jurisdiction to find her not eligible and remove her from the ballot. It would get fast-tracked to SCOTUS for certain!
And Harris' constitutional eligibility would likely be confirmed in a 9-0 decision but at least the matter will have finally been settled.
“...Harris’ constitutional eligibility would likely be confirmed in a 9-0 decision...”
Just give Alito a chance!