But the case could serve to amplify claims made by President Donald Trump that late-arriving ballots and drawn out electoral counts undermine confidence in elections.
Illinois is among 18 states and the District of Columbia that accept mailed ballots received after Election Day as long they are postmarked on or before that date, according to the National Conference of State Legislatures.
In March, Trump signed a sweeping executive order on elections that aims to require votes to be "cast and received" by Election Day and says federal funding should be conditional on state compliance.
In their appeal to the court, the Illinois Republicans said the justices should make clear that candidates have the right to challenge state regulations of federal elections.