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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 SebeliusJerry Moran: 'I wouldn't be surprised' if Pompeo ran for Senate in Kansas Mark Halperin inks book deal 2020 Democrats fight to claim Obama's mantle on health care MORE, Deputy U.S. Attorney General Jim Cole, Sen. Tim KaineTimothy (Tim) Michael KaineSen. Kaine: No reason for US to 'engage in military action to protect Saudi oil' Bolton exit provokes questions about Trump shift on Iran Overnight Defense: Dems grill Trump Army, Air Force picks | House chair subpoenas Trump Afghanistan negotiator | Trump officials release military aid to Ukraine MORE (D-Va.) and Congressman Bobby ScottRobert (Bobby) Cortez ScottHouse panel delays vote on surprise medical bills legislation Ten notable Democrats who do not favor impeachment Critics fear widespread damage from Trump 'public charge' 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 Emiel FeinsteinGOP's Kennedy sends warning shot to Trump nominee Menashi Democratic senators quietly hope Biden wins over rivals Grassley: Kavanaugh classmate didn't contact Senate panel 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.