Vice President Biden expects to deliver a package of gun control measures to President Obama by Tuesday, likely including new restrictions on guns and ammunition that the nation's largest gun rights lobby blasted following a White House meeting with Biden on Thursday.

Biden, who has been meeting with groups on both sides of the gun control debate, hinted at an emerging consensus around universal background checks for all gun owners and a ban on high-capacity ammunition magazines.

"There is a ... surprising recurrence of suggestions that we have universal background checks," the vice president said. "I've never quite heard as much talk about the need to do something about high-capacity magazines as I've heard spontaneously from every group that I've met with so far."

Biden was assigned to devise an administration strategy for reducing gun violence following the Dec. 14 massacre of 20 children at a Connecticut elementary school. President Obama pledged after the mass killing to push the gun control measures Biden proposes in Congress in coming months.

Biden invited the National Rifle Association to a White House meeting Thursday, and it was clear just minutes after the private meeting ended that any cooperation between the administration and the NRA is highly unlikely.

"We were disappointed with how little this meeting had to do with keeping our children safe and how much it had to do with an agenda to attack the Second Amendment," the NRA said in a statement. "We will not allow law-abiding gun owners to be blamed for the acts of criminals and madmen."

The NRA, which recommended posting armed guards at schools following the Connecticut shooting, said that rather than work with the White House, it would meet with lawmakers interested in "having an honest conversation about what works and what does not."

Gun control advocates cautioned the president not to fear the NRA's Capitol Hill clout, which has been strong enough to allow the group to kill virtually every attempt to toughen the nation's gun laws.

"The NRA is not nearly as invincible as was once believed based upon the fact that the NRA lost all but one of the Senate seats it targeted with millions in campaign cash," said Daniel Webster, director of the Johns Hopkins Center for Gun Policy and Research. "NRA members and gun owners are smart enough to know that requiring someone to undergo and pass a criminal background check before they take possession of a firearm does not violate anyone's constitutional rights. It's just common sense."

Biden riled the NRA and other gun rights advocates earlier this week when he suggested Obama could impose new gun restrictions by executive order, bypassing Congress altogether.

But the vice president also said the proposals Obama sends to Capitol Hill will go far beyond gun restrictions. Obama would also address ways to improve mental health services and reduce violent content in popular culture, Biden said. He added that the federal government needed to expand its research on gun violence, enhancing its ability to track "what kinds of weapons are used most to kill people."

Underscoring the urgency of the issue, Biden was outlining developments in his talks Thursday when news broke of another school shooting. A California high school student had opened fire with a shotgun, wounding a classmate before surrendering the weapon.