"It is clear that he has a strong understanding of economic and budgetary policy and, he knows firsthand how to create fiscal policies that work for middle class families and help our economy grow."
Murray said she is hoping the Senate will quickly approve his nomination.
Deese, who is the deputy director of the National Economic Council, also would play a role in the Office of Information and Regulatory Affairs (OIRA), which reviews agency regulations before final approval.
OIRA has been criticized for a lack of transparency and delaying rule implementation.
During his nomination hearing on May 21, Deese said while regulatory oversight was "not an issue that I've been closely involved in," he pledged "to bring fresh eyes and try to ask the set of questions about what could we do to improve the transparency and also the rigor of the process."
Deese would take over for Heather Higginbottom, who left the OMB to work for Secretary of State John Kerry in February.