(CBS NEWS) -- With a self-imposed end of January deadline to come up with a proposal regarding gun safety, Vice President Biden is accelerating efforts of the White House task force on gun violence with a series of meetings this week.

The president created the task force shortly after the mass shootings in Newtown, Conn., last month. He appointed Biden as the head of the task force and asked for recommendations by the end of January.

Upon returning from his long weekend in the U.S. Virgin Islands, Biden has numerous task force-related meetings scheduled this week. He will meet with officials of the video game industry and mental health experts, which the president said are important factors to examining gun violence. Additionally, Biden will meet with illegal gun opponents and pro-gun groups, including the National Rifle Association, in an effort to seek input and build consent for action, CBSNews.com has confirmed.

"We look forward to hearing from a variety of organizations," White House spokesman Jay Carney said Tuesday. 

President Obama has indicated that he wants Congress to reestablish the ban on assault weapons, which expired in 2004, and limit the size of magazines and expand background checks, including closing the gun show loophole, which allows unlicensed sellers to sidestep checks.The task force is also expected to look at broader efforts that might include a national database and proposals that can be implemented without congressional approval, the Washington Post reported.

Biden has also been conferring with New York City Mayor Michael Bloomberg, who is a vocal advocate for gun regulation. His group, Mayors Against Illegal Guns, launched a TV ad Tuesday to pressure lawmakers to "stand up to the gun lobby."

Roxanne Green, whose daughter was killed in the 2011 Tucson, Ariz., shooting that injured former Rep. Gabrielle Giffords, D-Ariz., is highlighted in the ad. "I have one question for political leaders, when will you find the courage to stand up to the gun lobby? Whose child has to die next?" Green says.

The timing of the ad is intentional, not only to keep the pressure on lawmakers to act in the aftermath of the Newtown massacre, but because it is also debuting on the second anniversary of the Tucson shooting.

Also Tuesday, Giffords and her husband, Mark Kelly, launched a new organization,Americans for Responsible Solutions, in favor of gun restrictions that intends to "[match] gun lobbyists in their reach and resources," the couple wrote in a USA Today op-ed.

When gun safety advocates refer to the gun lobby, there are numerous organizations that promote less gun regulation, but the most powerful is the National Rifle Association, which has spent nearly $10 million since President Obama's inauguration on lobbying activity, according to the Center for Responsive Politics. That number doesn't include the more than $30 million the NRA's political action committee and the organization's affiliated political nonprofits spent to influence the 2012 presidential and congressional elections. 

The NRA has proposed placing armed guards in schools to clamp down on shootings. It's a proposal the president has rejected.

Despite efforts to maintain momentum on the gun issue, Senate Minority Leader Mitch McConnell, R-Ky., said over the weekend that Congress must prioritize its early March deadlines around spending cuts and the debt ceiling. "Clearly we will not be addressing that issue early, because spending and debt are going to dominate the first three months," McConnell said Sunday on CBS' "Face the Nation."