Abramson was elected to the LouisianaHouse of Representatives during the 2007 general election with 74% of the vote defeating Democrat James P. Johnson. On October 22, 2011, Abramson won re-election to District 98 again with 74% of the vote after defeating Republican John French. Abramson was re-elected for a third term in 2015 without opposition. Abramson served on the following committees during his time as Representative: Ways and Means, Civil Law and Procedure, select Committee on Hurricane Recovery, Health and Welfare, Judiciary, Joint Legislative Committee on Capital Outlay, Joint Legislative Committee on Budget, and State Bond Commission. He served as Chairman of the Committee on Ways and Means, and previously served as Chairman of the Joint Legislative Committee on Capital Outlay, Chairman of the Committee on Civil Law and Procedure, Chairman of the Select Committee on Hurricane Recovery, and Vice Chair of Judiciary from 2007–2011. In 2012, Representative Abramson conveyed updates on Hurricane Isaac to his constituents via Twitter. In 2016, Representative Abramson was criticized by the Orleans Parish Executive Democratic Committee for his vote on the Speaker's race in 2015. The committee did not invite Abramson to the meeting, give him prior notice or hear the complete story. The Committee's choice for Speaker did not have enough votes to win prior to election. Abramson supported the candidate chosen by the majority of the House of Representatives, which was better for Abramson's constituents and district.
Notable legislation
Through his career, Abramson championed legislation seeking to improve mental health access and treatment, to stop human trafficking and to promote early childhood education. As a result, legislation authored and passed by Abramson on human trafficking, Louisiana now leads the nation with the highest grade for its human trafficking laws based on industry group assessments. Abramson also authored and passed legislation for the safety and protection of the state's youth by requiring in-service training related to suicide prevention for nonpublic and charter school teachers and other employees. Abramson has also been focused through his legislative tenure on reforming the state's fiscal affairs. As Chairman of Ways and Means, Abramson led the way in changing the state's Capital Outlay Process, which included eliminating the previous structural deficit in that budget. Throughout Abramson's tenure, he has been an advocate for reforming the state's on-going structural deficits in its operating budget through a limited constitutional convention focused solely on fiscal matters. Stating that, "A limited state constitutional convention would allow for a comprehensive re-work of the state tax structure and state budget system as well as to restructure the current state-local financial system."