U.S. lawmakers are likely to take a piece-by-piece approach to legislation aimed at combating gun violence, as a comprehensive package of gun laws could be a tough sell to a bitterly divided Congress, experts said Thursday.

President Barack Obama unveiled a rash of new proposals Wednesday aimed at curbing gun violence after last month' s horrific massacre in Newtown Connecticut that left 20 elementary school students dead and shocked nations worldwide. Measures included a ten-round limit on gun magazines, a ban on assault weapons, a clampdown on gun trafficking and better background checks.

Lanae Erickson Hatalsky, director of social policy and politics at Third Way, noted Obama did not make the package comprehensive, but instead said it could be done bit-by-bit.

That was a smart move for Democrats, she said, since proposals such as improving the background check system, for example, could find agreement on both sides of the political divide.

"There are a lot of pieces that (Obama) suggested that would go a long way toward reducing gun crime," said Hatalsky.

Those include stricter penalties for gun traffickers. Currently, there are no federal laws against gun trafficking, only state laws, which ties the hands of law enforcement. And while there is a law against selling a firearm to a known felon, it is difficult for prosecutors to use it in court.

"That means you can drive a truck full of weapons into a city and sell them in an alleyway to a stranger and fear no prosecution from the federal government," she said, although state laws could come into play under such a scenario.

So far, the weeks following the shooting have seen a firestorm of debate between leading Democrats calling for a ban on assault weapons and gun proponents who maintain that such a ban would infringe on Americans' constitutional right to bear arms.

Indeed, Obama' s proposed ban on assault weapons is likely to face an uphill climb in the GOP-controlled House and strong opposition from the National Rifle Association, whose president, David Keene, told ABC News Wednesday that the gun lobby is preparing for "battle" with the White House and Congress.

Florida Sen. Marco Rubio said Wednesday that Obama' s proposals would fail to stop another Newtown-style killing spree, and some conservative pundits argue the White House proposals failed to address holes in the mental health system, as well as violence in the U.S. film and video game industries.

Questions of constitutionality will play a pivotal role.

The office of Senate Minority Leader Mitch McConnell said Wednesday the first test of any new legislation the majority leader decides to bring before the Senate "will be on whether or not it infringes on the constitutional rights of law-abiding citizens to keep and bear arms."

For now, it remains unclear what the Senate Judiciary Committee will consider, sources familiar with the matter said.