The U.S. president linked the secretary of state's future attention to the island to his work on Russia and Ukraine, without announcing new measures during the speech.
Roma explained its abstention at the UN with criticism of the Cuban government's decisions, although it also called for the elimination of the embargo and recognized its effects on the population.
National polls gave Democrats 64 percent support among Hispanic voters, while an earlier survey of Cuban Americans in Miami-Dade put intended support for Republican candidates at 68 percent.
The proposals include salary cuts of up to 20% for nonunion employees. City Hall confirmed the discussions but said no measure has received final approval.
Miller will replace Susie Wiles effective November 9. He moves up from deputy chief of staff after years of influence over the president's immigration agenda.
The package covers eight companies and two individuals and restricts operations involving five oil tankers connected with crude transport.
