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Voters are likely to feel passionately about the plan, with nearly seven in 10 saying they have a "strongly" favorable (38 percent) or "strongly" unfavorable (31 percent) sentiment toward the president's proposal. Support is strongly split along partisan lines; more than three-quarters of Democrats support the president's plan, while a full 72 percent oppose it.

A majority of independents do favor Obama's plan, with 51 percent saying they have a favorable opinion. By contrast, 44 percent said they had an unfavorable view.

The president is looking to grow that support, dispatching Vice President Biden to an event Friday at Virginia Commonwealth University to promote the plan. Biden will be joined by Secretary of Homeland Security Janet Napolitano, Secretary of Health and Human Services Kathleen SebeliusKathleen SebeliusObama's health secretary to be first female president of American University Leaked email: Podesta pushed Tom Steyer for Obama’s Cabinet Romney: Trump victory 'very possible' MORE, Deputy U.S. Attorney General Jim Cole, Sen. Tim KaineTim KaineA guide to the committees: Senate Mattis on rise in Trump administration Senate advances Trump's Commerce pick MORE (D-Va.) and Congressman Bobby ScottBobby ScottA guide to the committees: House Repeal without replacement: A bad strategy for kids House Dems press Trump for details on ObamaCare order MORE (D-Va.)

On Wednesday, White House press secretary Jay Carney said the president was likely to begin traveling soon to host campaign-style events of his own in support of his policy agenda.

"I think you can fully expect that his commitment to engaging the American people in these important discussions about our future will continue," Carney said.

On Thursday, Sen. Dianne FeinsteinDianne FeinsteinA guide to the committees: Senate Dem: Trump's China trademark looks like a quid pro quo Senate advances Trump's Commerce pick MORE (D-Calif.) introduced an updated assault-weapons ban in the Senate that would ban the sale and manufacture of more than 150 types of semi-automatic weapons with military-style features. The bill would also ban magazines holding more than 10 rounds of ammunition.

“Getting this bill signed into law will be an uphill battle, and I recognize that — but it’s a battle worth having,” Feinstein said. “We must balance the desire of a few to own military-style assault weapons with the growing threat to lives across America.”

-- Alexander Bolton contributed.