But it also uncovered a sense of apprehension among likely voters about where the United States will stand relative to its global competitors in the coming decades.
One-quarter of likely voters said that China will take the No. 1 position with regard to science and technology, the poll found.
Public research funding has come under scrutiny as Republicans in Congress seek to reduce the budget deficit.
The "sequester" — automatic spending cuts set to take effect in January — will hit research investments at the National Institutes of Health (NIH) and the Centers for Disease Control (CDC) unless lawmakers stop it.
Research!America CEO Mary Woolley said that across-the-board cuts to medical research will have unintended consequences for millions of patients.
"Our polling shows that likely voters are fully aware of the fiscal challenges facing the nation, but feel strongly that funding for medical research should be a priority for candidates and elected officials," Woolley said in a statement.
Just over half of likely voters said that across-the-board cuts such as the sequester are not the right way to reduce the deficit, the poll found. Forty-nine percent said that the United States should not scale back its funding for medical research.
In total, the sequester would reduce budgets at federal health agencies by $3.6 billion, according to a May report from Research!America.
At the NIH specifically, the mandated 7.8 percent cut would be equal to the total amount spent researching "hundreds of rare and common diseases and conditions" in 2011, the report stated.
The sequester is a product of the Budget Control Act of July 2011, which was meant to force lawmakers to agree on a major deficit reduction plan.