Sen. Heidi Heitkamp (D-N.D) on Sunday warned against pressing for excessive gun control regulations, cautioning that such measures wouldn't win passage from lawmakers on Capitol Hill.

"I think you need to put everything on the table, but what I hear from the administration -- and if the Washington Post is to be believed -- that's way, way in extreme of what I think is necessary or even should be talked about.  And it's not going to pass," Heitkamp said on ABC News's "This Week With George Stephanopoulos."

Hetikamp apparently was referring to a story in Sunday's Washington Post about the White House's decision to weigh a broader and more comprehensive approach to curbing the nation’s gun violence than reinstating bans on assault weapons and high-capacity ammunition.

Heitkamp, a freshman senator, has received an "A" rating from the National Rifle Association, the nation's largest gun-rights group. She said that addressing mental health issues should also be an important part of curbing mass violence.

"Let's start addressing the problem.  And to me, one of the issues that I think comes -- screams out of this is the issue of mental health and the care for the mentally ill in our country, especially the dangerously mentally ill.  And so we need to have a broad discussion before we start talking about gun control," Heitkamp said.

An Obama administration task force led by Vice President Biden plans to offer recommendations on how best to curb gun violence in the wake of the mass shooting at a Newtown, Conn., school. Boston Mayor Thomas Menino (D) recently said that Biden has told him that President Obama will pass sweeping firearms reforms by the end of the month, the Boston Herald reported.

Senate Minority Leader Mitch McConnell (R-Ky.), meanwhile, said Sunday that the debate over guns isn't as high a priority for Congress as dealing with the nation's spending and debt concerns.

"The biggest problem we have at the moment is spending and debt," McConnell said on "This Week." "That's going to dominate the Congress between now and the end of March. None of these issues, I think, will have the kind of priority that spending and debt are going to have over the next two or three months."

The debate over gun control was a topic of discussion elsewhere across the Sunday show landscape, with both advocates and opponents of tightening measures offering their input.

On CBS News's "Face The Nation," two members of the House who recently returned to Congress after being reelected in November disagreed about the need for a renewed ban on assault weapons.

"I’m a hunter--believe in Second Amendment rights. But you know what? I don’t need an assault weapon to shoot a duck," Rep. Rick Nolan (D-Minn.) said. "And I think they ought to be banned and I think we need to put a ban on the amount of shells you can carry in a magazine and I think we have to strengthen our background checks."

"I do not support the assault weapon ban," said Rep. Matt Salmon (R-Ariz.), on the same program. "I was here during the assault weapon ban. It happened in 1992, I was here during the assault weapon ban for six years and I remember when the Congresswoman from Columbine came into my office, weeping, and we prayed together that day. It was a terrible time. That happened right in the middle of the assault weapon ban. Let’s stop placating the American people and telling them we’re doing something when we’re really doing nothing."

Sen. Chris Murphy (D-Conn.), who said he's spent most of the last month with the families affected by the Newtown shooting, said he disagreed with McConnell's call to put off a debate about guns until after the the nation's spending and debt issues have been addressed.

"I don’t think we should wait three months to get this done. I think we should get it done now. And I frankly think that if we did that it would save lives," Murphy said on "Face The Nation."

Updated at 1:07 p.m.