In 2008, Nordquist ran for the Nebraska Legislature from District 7, representing downtown and southern Omaha. The incumbent, Synowiecki, was ineligible to run for a third consecutive term under Nebraska's term-limits law. Nordquist, a member of the Democratic Party, was opposed by Christopher Moles, a Republicanlaw clerk who was then working on a law degree and a master's degree in business administration at Creighton University. In the nonpartisan primary, Nordquist received 1230 of the 1835 votes cast, or 67%. Moles received 605 votes, or 33%. As the top two vote-getters in the primary, both candidates moved on to the November general election. Nordquist won this election with 4961 of the 6726 votes cast, or 73.8%; Moles received 1765 votes, or 26.2%. In 2012, Nordquist sought re-election to the Legislature. He faced two challengers. Christopher Geary, a Republican business owner, had unsuccessfully run for the Nebraska governorship in 2010; he had placed third in a three-way Republican primary, losing to incumbent governor Dave Heineman with 4.8% of the vote to Heineman's 89.9%. Adrian Petrescu, a professor of public policy at the University of Nebraska Omaha, was making his first bid for elective office. In the primary election, Nordquist received 1406 of the 1934 votes cast, or 72.7%. Geary placed second, with 345 votes, or 17.8%; Petrescu received 183 votes, or 9.5%. As the top two vote-getters, Nordquist and Geary moved on to the general election. Nordquist won re-election with 4211 of the 6003 votes cast, or 70.1%; Geary received 1792 votes, or 29.9%. During his tenure in the Legislature, Nordquist served as chair of the Retirement Systems Committee; he also sat on the Appropriations Committee. In 2014, he co-chaired an initiative petition drive that sought to raise the state's minimum wage to $9 per hour; the measure passed in the general election. In 2015, Nordquist resigned from the Legislature in order to become chief of staff for Brad Ashford, who had been elected to represent Nebraska's 2nd District in the U.S. House of Representatives. Republican governor Pete Ricketts appointed Nicole Fox, a Republican, to serve the remainder of the term.
Policies
Deferred Action for Childhood Arrivals
Nordquist was the lead co-sponsor of a bill which would allow DACA recipients to receive driver's licenses. 623.
State minimum wage
Nordquist led a successful initiative to increase the state minimum wage to $9 per hour by 2016. 135,000 Nebraskans signed a petition to put the initiative on the ballot in 2014, which was voted on in the November 2014 election. He also attempted unsuccessfully to persuade the legislature to raise the minimum wage for tipped workers.
LGBT rights
In 2013 and 2015, Nordquist sponsored multiple bills to protect or expand LGBT rights while serving in the legislature. One bill would prevent discrimination in employment and housing by adding sexual and gender identity to the classes protected from discrimination in employment, housing, and public accommodation. Another pair of bills would allow same-sex couples to adopt children or become foster parents, overturning a 20-year old policy which only permitted married heterosexual couples to adopt or serve as foster parents. Each time, the bills were eventually tabled due to stiff opposition from the religious lobby.
