Demonstrators protest the visit of US President Donald Trump to the site of the mass shooting in Dayton, Ohio, on August 7, 2019.

Gun control advocacy groups have dedicated more than $2 million on digital and TV ads, widely outspending the National Rifle Association, since the mass shootings weeks ago in California, Texas and Ohio that left more than 30 dead.

Everytown for Gun Safety — funded mostly by Michael Bloomberg, the billionaire and former New York mayor — is leading the way with a $935,000 ad campaign. Its digital and TV ads call on Congress to require tougher background checks for gun sales along with strong red-flag laws, which are meant to take firearms away from those deemed a threat to themselves or others.

The NRA has spent just $14,000 on Facebook ads since last week. Instead, the group focused its recent advocacy on tweeting and being in direct contact with President Donald Trump.

Gun control advocates say the NRA may not spend as much for lobbying going forward because they have Trump's ear.

"There is not a response from them to counter the overwhelming push from the American people, politicians and activists on this issue," said Andrew Patrick, media director at the Coalition to Stop Gun Violence. "In the past, they get their lobbying going. Now they can call the president and he can prepare their talking points."

The spate of shootings has given organizations calling for tighter gun laws new momentum, particularly as big-money backers such as Bloomberg look to counter the decades-long influence the NRA has exerted on Capitol Hill.

Everytown for Gun Safety's campaign focuses largely on Republican senators who have resisted calls for tighter gun control. They include Senate Majority Leader Mitch McConnell, of Kentucky, and Sens. Marco Rubio and Rick Scott, both of Florida, Richard Burr, of North Carolina, and John Cornyn, of Texas. Most of these lawmakers have previously received NRA contributions. The ads will start airing next week and will continue through the August recess.

Shannon Watts, founder of Moms Demand Action for Gun Sense in America, which is part of the Everytown group, says Senate lawmakers will have to listen or expect to face tough reelection battles.

"We're hopeful that the Senate will act, but if they don't there will be hell to pay in 2020," Watts told CNBC on Thursday. "We are having our events in all 50 states, and it's really important that senators in red, blue and purple states listen to these constituents," she added. The organization is also spending $65,000 on nationwide rallies that are scheduled to take place this weekend.

A Fox News poll taken Aug. 11-13 showed that 90% of participants support requiring all potential gun buyers to go through a criminal background check, while 81% said they'd like red-flag laws.

Sandy Hook Promise, a nonprofit organization created by the families of victims of the 2012 gun massacre at an elementary school in Connecticut, has spent just over $300,000 on Facebook ads since Aug. 7, according to the company's ad library. The most recent ad shows a boy named Dylan, who was killed during the mass shooting, and calls on Congress to limit the size of gun magazines.

Only billionaire and presidential candidate Tom Steyer, with more than $900,000 in ads over the past seven days, has spent more than Sandy Hook Promise on Facebook ads.

Ban Assault Weapons NOW, a nonprofit whose leadership includes survivors of various mass shootings, has spent just over $90,000 on ads since this summer's mass shootings. Its latest message calls for people to sign its petition urging a ban on assault weapons in Florida. It also criticizes Congress for its inaction on gun laws and its members' ties to the NRA.

A gun control advocacy group founded by former Rep. Gabrielle Giffords, who was shot in the head during a mass shooting in Arizona in 2011, has launched a $750,000 TV ad campaign. It will call for McConnell and Sen. Cory Gardner, of Colorado, to support background-check legislation.

While the NRA hasn't spent much recently, it has used other means to get its message across.