The bill will not include other aspects of the plan introduced by the president in the aftermath of the Newtown, Conn., shooting, including the renewal of an assault weapons ban or limits on magazine capacity — although Senate Majority Leader Harry ReidHarry Mason ReidWhite House races clock to beat GOP attacks Harry Reid reacts to Boehner book excerpt: 'We didn't mince words' The Memo: Biden seeks a secret weapon — GOP voters MORE (D-Nev.) has pledged to allow a vote on those provisions as an amendment. 

On Tuesday, the White House announced President Obama will travel to Connecticut on Monday in his latest effort to push the Senate to act on a set of new gun control proposals.

"He will continue asking the American people to join him in calling on Congress to pass common-sense legislation to reduce gun violence," White House press secretary Jay Carney said Tuesday.

The administration has intensified efforts to build momentum for the gun package ahead of a planned Senate vote following the Easter recess. On Wednesday, Obama will travel to Colorado and visit the site of the Aurora, Colo., movie theater shooting. Families of victims of gun violence, including relatives of some who died in the Newtown shooting, also attended the White House Easter Egg Roll on Monday.

The "Morning Joe" poll also found support for the president's economic agenda. Obama edges congressional Republicans by a 44-40 percent margin on who has the better approach to deal with the federal budget deficit. Moreover, 42 percent back the president's proposal to address the deficit through a mixture of spending cuts and revenue increases, while just 17 percent say deficit reduction should be achieved solely through cutting government spending. 

Respondents also said, by a nearly two-to-one margin, that lawmakers should emphasize job creation over deficit reduction.