WASHINGTON—The Supreme Court appeared as split as the nation over immigration policy Monday, with the justices divided over a 26-state challenge to Obama administration plans for deferring deportation of some four million illegal immigrants whose children are U.S. citizens.

Four conservative justices at oral arguments in the case appeared critical of the plan, called Deferred Action for Parents of Americans, which lower courts temporarily blocked after Texas filed its challenge on behalf of Republican-leaning states. Four...