(CNN) – Vice President Joe Biden's package of proposals on gun control – collected after meetings with various constituencies, including gun rights groups, retailers, and video game manufacturers – combines both "administrative actions" that the White House can take unilaterally and measures that will be presented to lawmakers in Congress, according to Democratic lawmakers who met with Biden this week.
The collection of measures includes 19 steps President Barack Obama can take himself using executive action, according to Rep. Jackie Speier, a member of the Democratic gun violence task force that met with Biden Monday.
"He didn't go into all of them," Speier said on CNN's "Newsroom with Brooke Baldwin." "Certainly they will be considered by the president."
A Democratic member of Congress who attended the meeting with Biden Monday said some of the 19 executive actions discussed include improving the way the government administers current law - for example, the database used for background checks during gun sales has information gaps, including on mental health. Improving that could be considered an "executive action."
Rep. Mike Thompson, who chaired the Democratic gun task force that met with Biden, detailed some of what the vice president's package contains on Tuesday's "Starting Point with Soledad O'Brien" on CNN.
"We met with the vice president yesterday, and the vice president said we need a comprehensive package to put an end or help put an end to the gun violence," Thompson said. "Congress is going to be important. It's going to be a cooperative effort with the two branches of government."
The "administrative actions" which Thompson said Obama could begin pursuing immediately include appointing a director of the Bureau of Alcohol, Tobacco, Firearms and Explosives, which has been without a permanent chief for six years. The acting director, B. Todd Jones, also serves as the U.S. attorney in Minnesota.
Thompson said Obama could also demand federal agencies provide data for background checks that are supposed to accompany gun sales, ensuring the information included in the checks is as "comprehensive and complete as possible."
Obama has not ruled out issuing executive orders on some gun control measures to enforce laws already on the books, such as bolstering the way gun sales are tracked. At a news conference Monday, Obama reiterated his desire for more robust background checks for gun buyers, keeping high capacity magazines away from criminals, and a ban on assault weapons.
"Will all of them get through this Congress? I don't know," Obama said. "But what's uppermost in my mind is making sure that I'm honest with the American people and members of Congress about what I think will work, what I think is something that will make a difference."
Obama said Monday he had begun reviewing Biden's package and would make concrete proposals later this week. Obama and Biden will meet for lunch Tuesday at the White House.
Working with Congress will be paramount in curbing gun violence, Thompson said Tuesday, singling out a ban on high capacity magazines as an example of a measure that could garner Republican support. A full-scale assault weapon ban would be tougher to pass the GOP-controlled House, he argued.
"I think we have to concentrate on what is most important in saving lives. If you take the assault magazine out of the rifle, the rifle will have less capacity than it would have otherwise. I think that is absolutely important. We need to prioritize on this," Thompson said.
CNN Chief White House Correspondent Jessica Yellin contributed to this report.