WASHINGTON — Vice President Joe Biden said Thursday that he’s more concerned about limiting the number of rounds in a gun magazine than about banning assault weapons that account for a small percentage of gun deaths.

Biden argued that the shooter at the Sandy Hook Elementary School in Newtown, Conn., could have been slowed down if he had fewer rounds in each magazine and had to change clips more often. “Maybe if it took longer, maybe one more kid would be alive,” Biden said during an online video chat on Google Plus.

The vice president led a White House gun control task force in the wake of the Newtown shooting last month. President Barack Obama said last week after Biden completed the review that he wants Congress to require background checks for all gun sales and ban both military-style assault weapons and high-capacity ammunition magazines. The president conceded passage will be difficult, with support for gun ownership rights strong among lawmakers.

Biden says he wants a ban on assault weapons, even though he acknowledges they don’t account for a large portion of gun deaths in America. He says a ban would solve part of the gun violence problem, particularly for police who can be outgunned by criminals with assault weapons.

“It is not an answer to all the problems,” Biden said. But he said he views an assault-weapons ban as “a rational limitation on what type of weapons should be owned.”

Biden’s comments came on the same day that a group of Democratic lawmakers, led by Sen. Dianne Feinstein of California, reintroduced legislation to ban assault weapons and magazines over 10 rounds. At a news conference backed by police officials, mayors and crime victims, the lawmakers acknowledged the heavy lift ahead to get the legislation through Congress.

“If anyone asks today ‘Can you win this?,’ we don’t know, it’s so uphill,” Feinstein said. She said it only would happen if voters got behind the measures and called on their lawmakers to act.

Feinstein authored the original assault-weapons ban in 1994 which expired 10 years later when Congress, under pressure from the National Rifle Association, refused to extend it. There is debate about its effectiveness during the years it was in effect, in part because of loopholes that allowed gun manufacturers to work around it. Feinstein’s new version is more comprehensive in defining what kinds of weapons are banned.

The NRA responded that the new bill would infringe on the Constitutional right to bear arms and that instead the focus should be on prosecuting criminals and improving the country’s mental health system. “The American people know gun bans do not work, and we are confident Congress will reject Sen. Feinstein’s wrong-headed approach,” the NRA said in a statement.

At Feinstein’s press conference, nearly a dozen different kinds of high-powered weapons were displayed that would be banned by the bill, including the kind of Bushmaster used in the Connecticut shooting.

The assault weapons ban in particular is seen as unlikely to make it through Congress, because of opposition by majority Republicans in the House and concerns from moderate Democrats in the Senate. Even Senate Majority Leader Harry Reid, D-Nev., has cast doubt on its prospects. Some advocacy groups are focusing their attention instead on expanding background checks, which is seen as more doable politically.

Feinstein said those Democrats with concerns about the legislation needed to ask themselves what their silence would mean.

“Sandy Hook is more eloquent testimony than any of us could possibly give,” she said. “If members of this body are so insensitive to what happened to those small bodies from that Bushmaster when it all becomes known, America is hopeless.”

Biden is launching the White House’s promotional tour on gun control Friday with a trip to Virginia, a state that has experienced its own school shooting tragedy yet maintains an avidly pro-gun tradition. His office said Biden will hold a roundtable discussion in Richmond with experts who worked on gun safety in the wake of the 2007 shooting at Virginia Tech.

Biden will be accompanied by Homeland Security Secretary Janet Napolitano, Health and Human Services Secretary Kathleen Sebelius, Deputy U.S. Attorney General Jim Cole and other administration officials, as well as Sen. Tim Kaine and Rep. Bobby Scott, both Virginia Democrats.