Barnett was the chairman of the HousePublic Transportation Committee and served on these House committee: Advanced Communications and Information Technology, Budget, and Insurance and Commerce. Representative Barnett in 2013 co-sponsored a spending cap on state spending, but the measure failed by two House votes. He voted to override Governor Mike Beebe's vetoes of bills to prohibit abortion after twenty weeks of gestation. He supported other pro-life measures, including the ban of abortion once fetal heartbeat is detected, the prohibition of abortion coverage in state employees health insurance plans, and the classification of the death of an unborn child as a felony in certain situations. He voted to override Beebe's veto of the bill requiring photo identification as a condition for voting in Arkansas. Barnett co-sponsored the measures to allow the staff of religious institutions and universities to engage in concealed carry of firearms for church and campus safety. Barnett backed legislation to prohibit the governor from regulating firearms during an emergency. He supported the bill, signed by Governor Beebe, to permit the sale of five hundred gallons of milk per month directly from the farm to consumers. He voted to establish the tiered system for lottery scholarships. He voted against making the officeprosecuting attorney a nonpartisan position. In 2011, Barnett co-sponsored the Capital Gains Reduction Act and the reduction of taxes on manufacturers' utilities. He supported the implementation of school dress codes but objected to the banning of cell phone usage in school zones; both measures were approved by the House. He voted to require that driver's license tests be given only in the English language. Barnett did not vote on the bill establishing curriculum standards for Bible instruction in public schools nor on the 2011 U.S. congressional redistricting bill. In 2009, Representative Barnett supported the expansion of eligibility for children's health insurance. He voted against He voted against allowing unlicensed assistants to perform simple medical procedures. Both measures were passed by the House. In the Republican primary held on May 20, 2014, Robin Lundstrum, with 1,588 votes, defeated intraparty rival Lucas Roebuck, who polled 1,176 votes, for the party's nomination to succeed Barnett.
