A federal anti-cellphone-driving law would probably be (allegedly) justified by appeal to Congress's jurisdiction of interstate commerce.
Almost anything can be and does get justified as federal jurisdiction by the assertion of "interstate commerce". Want to have a law that a hot dog vendor on wheels should be federally regulated as to the hours worked by the salesman? The sausages of hot dogs are manufactured, sold, and shipped interstate. Voila, federal jurisdiction!
"Automobiles might travel across state lines; thus there's a claim of interstate commerce! So Congress needs to have a nationwide law against cellphone use while driving!" If such a law is proposed, depend on it, that claim will be advanced in support of its passage. "Promote the general welfare" is too general and vague for the purpose, but interstate commerce is sure to be claimed.