The NRA contends that an expanded background check system would create a paper trail that could eventually be used to build a national gun registry, which they reject as unconstitutional.
It also argues that an expanded system would prove a burden to law-abiding gun owners while doing nothing to stop criminals from getting hold of firearms.
According to a summary of the compromise proposal, it includes language that prohibits creation of a national gun registry or misusing information from background checks.
The NRA said rejection of the universal checks sought by Obama was "a positive development," and it called for "serious and meaningful solutions" to gun violence instead of "blaming law-abiding gun owners for the acts of psychopathic murderers."
Meanwhile, Obama said there were aspects of the Manchin-Toomey compromise that he would like to see strengthened.
"But the agreement does represent welcome and significant bipartisan progress. It recognizes that there are good people on both sides of this issue, and we don't have to agree on everything to know that we've got to do something to stem the tide of gun violence," the president said in a statement Wednesday.
"Congress needs to finish the job," Obama added, saying he would continue "asking the American people to stand up and raise their voices because these measures deserve a vote."
Other reaction ranged from cautious support to angry rejection.
The Brady Campaign, named after the former White House press secretary wounded in an assassination attempt on President Ronald Reagan, called the compromise a "good step forward," while New York Gov. Andrew Cuomo described it as "better than nothing" but a sellout to the gun lobby.
"This is a Congress that is captive of the extremists and there is no clearer proof of that than this," Cuomo said on the "Capitol Pressroom" radio show, adding that the compromise meant "we are not talking about a significant package of gun control anymore."
Obama has made gun measures a major focus of his second-term agenda, holding events across the country to push for Congress to vote on the package.
A new national survey showed that 86% of Americans support some expansion of background checks.
At the same time, the CNN/ORC International poll released Wednesday also showed a majority of respondents fear that increased background checks would lead to a federal registry of gun owners that could allow the government to take away legally owned weapons.
Failing to pass new gun laws would be a stinging defeat for Obama and Democrats.
However, a public perception that Republicans blocked popular proposals, such as expanding background checks, could harm GOP prospects in 2014 and 2016 among moderates they need in their corner to have any chance of countering strong support for Democrats by minority demographics such as Hispanic Americans, African Americans and the gay-lesbian vote.
The Senate Judiciary Committee passed a package of gun laws proposed by Obama after the Newtown attack by a lone gunman.
Proposals in the committee's package included expanding background checks on gun buyers, toughening laws against gun trafficking and straw purchases, banning semiautomatic rifles modeled after military assault weapons as well as large-capacity ammunition magazines, and coming up with ideas for improving school safety.
Reid dropped the weapons ban, which would update a similar 1994 law that expired a decade later, saying it lacked enough support to overcome a filibuster.
Some states already have passed stricter gun laws similar to the federal proposals since the Newtown shootings. They include Connecticut, where the killings occurred, and Colorado, the site of two other notorious mass shootings that contributed to a renewed gun debate in America.
The current background check system was created in 1989. It requires federally approved gun dealers to check whether gun buyers have a criminal background or other problem to make them ineligible to purchase a firearm.
Under the system, the gun dealer maintains a record of the transaction, but the federal government keeps no such identifying paperwork.
According to a Justice Department report, less than 2% of those seeking to purchase firearms were denied because of background checks from 1998 through 2009.
Opponents cite that figure as evidence that the system fails to stop illegal weapons sales that the legislation seeks to target, while supporters say the result shows the system keeps some guns out of the hands of the wrong people and the system should be expanded and strengthened.