Make Every Vote Count Act

Make Every Vote Count Act - Authorizes the Federal Election Commission (FEC) to award matching grants to encourage States and local voting areas to modernize applicable voting systems and enhance voter participation.

Amends the Soldiers' and Sailors' Civil Relief Act of 1940 to provide that, for purposes of voting for a Federal or State office, a person absent from a State in compliance with military or naval orders shall not, solely by reason of that absence, be deemed to have: (1) lost a residence or domicile in that State; (2) acquired a residence or domicile in any other State; or (3) become resident in or a resident of any other State.

Amends the Uniformed and Overseas Citizens Absentee Voting Act to require each State to: (1) permit absent uniformed services voters to use absentee registration procedures and to vote by absentee ballot in general, special, primary, and run-off elections for State and local offices; and (2) accept and process, with respect to any such election, any otherwise valid voter registration application from an absent uniformed services voter if the application is received by the appropriate State election official not less than 30 days before the election.