Obama gun control address live video: President live stream from Minneapolis police center

President Barack Obama headed to Minneapolis on Monday to discuss gun violence as the focus on possible legislation in the Senate appeared to narrow to expanded background checks and limited ammunition magazines, rather than a ban on semi-automatic rifles that mimic assault weapons.

The Wall Street Journal reported on Monday that an aide to Senate Majority Leader Harry Reid outlined such a measure that he wants the Judiciary Committee to draft.

Reid told ABC on Sunday that he backed expanding background checks to private gun sales at shows and other steps, but he refused to endorse a ban sought by Obama on what are called assault-style rifles modeled after military weapons.

A popular version is the AR-15 semi-automatic rifle that can be purchased with magazines holding 30 rounds. A similar weapon was used in the December Sandy Hook school massacre in Connecticut that killed 20 first graders and revived a national focus on tougher gun control measures.

While Obama and influential Democrats, including Sen. Dianne Feinstein of California, seek a ban on many semi-automatic rifles, the influential National Rifle Association and politicians from both major parties oppose such a move as an infringement on constitutional rights.

The volatile issue was the focus of an ad during Sunday night's Super Bowl by a group of mayors seeking stronger measures to halt gun violence.

Obama's trip to Minneapolis was intended to raise attention of steps taken in the city, including a recent regional gun summit hosted by the city's mayor, R.T. Rybak, and Milwaukee Mayor Tom Barrett.

Both cities have experienced mass shootings in recent months, and Obama met with two Minneapolis-area law enforcement officials last week when he discussed the issue with local police and sheriffs department members at the White House.

The NRA and its leading supporters in Congress argue that steps proposed by Obama won't work and would fail to address the problem.

For example, they say criminals skirt background checks, so expanding the system would miss the main target of the legislation. They also contend that the semi-automatic rifles targeted by Feinstein in a proposal introduced last week are used in a fraction of the nation's gun violence.

Obama and other supporters of stronger gun control measures say all possible efforts must be made to address what they call a chronic and growing problem of gun violence, particularly involving vulnerable targets such as students.

Reid is the top Senate Democrat, who sets the chamber's legislative schedule. He said Sunday that he wants the Judiciary Committee to produce a bill that could be debated by the full Senate and would be open to proposed amendments by any senator.

However, Reid signaled that the committee version would lack the ban on assault-style weapons.

"If Dianne Feinstein, by the time it's through the Judiciary Committee, if she doesn't have her assault weapons, at least let her have an opportunity to offer this amendment" on the Senate floor, Reid told ABC.

Reid, who noted he owned guns and was a former law officer, said he opposed the Clinton-era assault weapons ban that expired in 2004.

He called for expanding background checks and steps to halt federal gun trafficking while saying the Senate should "take a look at" unspecified limits on ammunition magazines.

Asked about backing he has received from the NRA, Reid said that "just because they resist it doesn't mean we can't do things."

Other steps under consideration include better monitoring of people with mental illness to prevent them from obtaining guns.

Last week, Vice President Joe Biden told reporters that Congress would be unable to totally eliminate gun deaths.

"Nothing we are going to do is fundamentally going to alter or eliminate the possibility of another mass shooting or guarantee that we will bring gun deaths down," Biden said after meeting with Democratic lawmakers on Capitol Hill.

After the Connecticut shootings, Biden led a panel assigned by Obama to look into the issue of gun violence. The president based his proposals on recommendations by Biden's panel.

Democrats have said the background check measure would stand the best chance of garnering bipartisan support, including from some pro-gun Democrats. Even if passed by the Senate, a gun bill would face tougher scrutiny in the Republican-led House.

Guns sold through private sales currently avoid background checks -- the so-called gun show loophole.

Democratic Sen. Chuck Schumer of New York said last week that he was in talks with colleagues -- including several who are ranked highly by the NRA -- on possible legislation to expand background checks on private gun sales.

Sources close to both Schumer and Republican Sen. Tom Coburn of Oklahoma told CNN the two were in serious discussions about co-sponsoring a bill to strengthen background checks. Schumer sits on the Judiciary Committee, while Coburn is a former member.

However, NRA chief executive Wayne LaPierre told the panel that the current background check system doesn't work, so expanding it would only create an unmanageable government bureaucracy instead of reducing gun crime.

During the Super Bowl on Sunday night, a group called Mayors Against Illegal Guns broadcast an ad showing the NRA's LaPierre, in 1999, endorsing the expanded background checks his group now opposes.

Supporters of gun control argue that the constitutional right to bear arms can be limited, for example, by the existing ban on private citizens possessing grenade launchers and other military weaponry.

However, Denver University law professor David Kopel said last week that the Supreme Court made clear that gun control could not include weapons used commonly by law-abiding citizens, such as the top-selling AR-15 that Feinstein's legislation would ban.

CNN's Kevin Liptak contribued to this report