Matthew Welsh began his career by becoming a member of the Democratic National Committee in 1964. He later returned to law practice and was appointed by President Johnson to the International Joint Commission, where he worked until 1970. Welsh then served on the Indiana Constitutional Revision Committee, authoring amendments that reorganized state courts and expanded the power of governors. Despite losing his bid for a second term as governor in 1972, his contributions to state governance and civil rights remain notable.

Matthew Welsh's political identity is marked by a blend of progressive civil rights advocacy and strategic governance reforms. His tenure on the Indiana Constitutional Revision Committee reveals a calculated effort to reshape state power dynamics. Welsh's economic policies, despite criticism, suggest a willingness to take bold steps, even if controversial. His unexpected alliances on environmental regulations hint at a nuanced approach to policymaking, balancing regional interests with broader goals.