The American statesman known for coining the phrase "The Great Compromise" was Roger Sherman during the Constitutional Convention of 1787. This compromise resolved debates between large and small states regarding legislative representation, leading to the establishment of a bicameral legislature with proportional representation in the House and equal representation in the Senate. Sherman's role in crafting this compromise was pivotal in ensuring the adoption of the U.S. Constitution, contributing to the balance of power between states and the federal government, which remains vital today.