Former Florida Gov. Jeb Bush, trailing in the polls, responded negatively to Obama's town hall, linking him to the Democratic front-runner.
"Look, any time that there's a crisis a tragedy, whether it's San Bernardino or these tragic mass killings by deranged people, the first impulse of the President of the United States and Hillary Clinton is to take more rights away from law-abiding citizens," Bush said in the minute-long video, which ends with the "Jeb!" campaign logo and a link to his campaign donation page.
GOP front-runner Donald Trump spoke to a packed Vermont crowd at the same time as the gun forum. The mogul reiterated a pledge to get rid of gun-free zones.
"There's no more gun free zones," Trump said to loud applause.
Other Republican candidates, from Texas Sen. Ted Cruz to New Jersey Gov. Chris Christie, were largely quiet on Twitter as Obama made his case to the public. And some, like Ben Carson, sent out pre-emptive tweets before Obama's town hall began.
"We need a President who will stop threatening legal gun owners, & start tackling the root causes of violent crime & terrorism in this county," the retired neurosurgeon tweeted.
Obama spoke for a little more than an hour Thursday night, fielding questions from supporters and opponents, during CNN's televised town hall, hosted by Anderson Cooper. Obama mocked opponents and others who he said were convinced he was coming for their guns.
The Republican National Committee, meanwhile, used the town hall as a fundraising and recruiting tool, tweeting out, "Obama's gun control policies bypass Congress & infringe on your #2A right. Protect it now."
Shortly before the town hall, House Speaker Paul Ryan tweeted, "Ahead of his town hall meeting, here are 5 things you need to know about the president's executive action on guns."
The new orders, he wrote, would not have prevented recent mass shootings, are not new, are designed to "intimidate" gun owners distract from Obama's "disastrous" policies and would not take away from the House's passage of a bill repealing the Affordable Care Act, which now goes to the President's desk.
Rep. Jim Bridenstine of Oklahoma, a supporter of Cruz and member of the conservative House Freedom Caucus, tweeted, "No one asked about whether a Social Security Admin. bureaucrat should decide who loses their constitutional rights? #GunsInAmerica"