A legal battle over when to wrap up the 2020 census is part of a broader push by the Trump administration to exclude illegal immigrants from the count that drives congressional reapportionment.

A series of court decisions in coming weeks will determine whether state population totals, which shape how many electoral votes each state receives, will be delivered during President Trump’s current term or will stretch into the spring, when a new administration could be in place. After initially asking for extra time to complete…