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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 SebeliusLeaked email: Podesta pushed Tom Steyer for Obama’s Cabinet Romney: Trump victory 'very possible' Fighting for assisted living facilities MORE, Deputy U.S. Attorney General Jim Cole, Sen. Tim KaineTim KaineDecaying DC bridge puts spotlight on Trump plan Booker to vote against Tillerson Senate Democrats brace for Trump era MORE (D-Va.) and Congressman Bobby ScottBobby ScottThe Hill's 12:30 Report House Dems may challenge Electoral College certification Dems press Trump to keep Obama overtime rule 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 FeinsteinJustice requires higher standard than Sessions Senate to vote Friday on Trump's defense picks Senate seeks deal on Trump nominees 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.