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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 SebeliusPrice was a disaster for HHS — Time for an administrator, not an ideologue Trump says he's unhappy with Price Former Health Secretary: Price’s use of chartered flights is 'stunning' MORE, Deputy U.S. Attorney General Jim Cole, Sen. Tim KaineTimothy Michael KaineAuthorizing military force is necessary, but insufficient Week ahead: Crunch time for defense bill’s cyber reforms | Equifax under scrutiny Insurer Anthem to cover bare ObamaCare counties in Virginia MORE (D-Va.) and Congressman Bobby ScottBobby ScottOvernight Regulation: SEC chief grilled over hack | Dems urge Labor chief to keep Obama overtime rule | Russia threatens Facebook over data storage law Dems call on DeVos to work with CFPB to protect student borrowers Dems offer alternative to Trump administration's child care proposal 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 Emiel FeinsteinGun proposal picks up GOP support Gingrich: Banning rapid fire gun modification is ‘common sense’ House bill set to reignite debate on warrantless surveillance 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.