"Presently, all global health funding faces potential cutbacks, with major budget cuts on the horizon due to sequestration and other fiscal pressures," the campaign wrote.
The U.S. contributed about 22 percent of the WHO's assessed budget for 2010 and 2011 and about 16 percent of its voluntary budget, according to the Government Accountability Office.
The BWC warned that a bid for Palestinian membership at the World Health Assembly in May could trigger a shutdown of U.S. funding for the WHO.
"While the Obama administration has no flexibility to waive the law, Congress has the power to grant the president waiver authority," the group wrote.
The poll was conducted Jan. 6-9 by Public Opinion Strategies and Hart Research Associates, and has a margin of error of about 3.3 percentage points.