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 SebeliusPro-dependency advocates miss the mark in attacking Kansas welfare reform Pence breaks tie to confirm Trump's pick for religious ambassador The House needs to help patients from being victimized by antiquated technology MORE, Deputy U.S. Attorney General Jim Cole, Sen. Tim KaineTimothy (Tim) Michael KaineBill to bolster gun background checks gains enough support to break filibuster Senators demand cyber deterrence strategy from Trump Two-year defense spending smooths the way to a ready military MORE (D-Va.) and Congressman Bobby ScottRobert (Bobby) Cortez ScottRyan, Pelosi name members to new budget and pension committees Overnight Health Care: Trump eases rules on insurance outside ObamaCare | HHS office on religious rights gets 300 complaints in a month | GOP chair eyes opioid bill vote by Memorial Day Overnight Regulation: Trump to take steps to ban bump stocks | Trump eases rules on insurance sold outside of ObamaCare | FCC to officially rescind net neutrality Thursday | Obama EPA chief: Reg rollback won't stand 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 FeinsteinWhat’s genius for Obama is scandal when it comes to Trump Coalition presses Transportation Dept. for stricter oversight of driverless cars Saudi energy deal push sparks nuclear weapon concerns 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.