Yet Donald Trump, the party's undisputed front-runner for six months, remains the only candidate unscathed so far.
Here's a look at some of the most recent spots.
Ted Cruz and Marco Rubio have been tussling for months, first over each other's immigration stances
and now over national security
On Monday, the super PAC backing Cruz released a new spot to paint Rubio, who has been dogged by questions about his Senate attendance record, as unserious. Using footage from a lighthearted video Rubio made, in which he jokingly confuses fantasy football players with presidential candidates of the same name, the attack ad
lists various threats against America before cutting to video of Rubio discussing fantasy football. The ad is set to run in Iowa for two weeks and is intended to blunt any potential last-minute surge by Rubio ahead of the caucuses.
Rubio, for his part, has been less aggressive going after Cruz on the airwaves in Iowa, instead devoting his focus to New Hampshire. But in stump speeches and interviews, Rubio frequently criticizes Cruz for his vote to reform the NSA surveillance program, which Rubio argues removed a valuable tool from counterterrorism efforts, and has used the vote to characterize Cruz as soft on security.
And a super PAC backing Rubio, Conservative Solutions, released an ad
Tuesday touting Rubio's electability that calls him "the one Hillary Clinton doesn't want to run against," an attempt to tweak Cruz over concerns about his general election viability due to his hardline conservatism.
Rubio vs. Christie
Cruz isn't the only candidate with whom Rubio is locking horns.
This week, the Florida senator's team released a flurry of attack ads against New Jersey Gov. Chris Christie, just as the brash governor is threatening Rubio's status as the GOP establishment's preferred candidate.
Rubio's super PAC, Conservative Solutions, put up two ads in New Hampshire, blasting Christie over his record in New Jersey. The first calls Christie "Obama's favorite Republican governor"
and criticizes his support for an Internet sales tax, the Common Core education initiative and 'liberal" energy policies.
The second ad
slams Christie for his unpopularity in his home state, and describes his term as governor in five words: "High taxes. Weak Economy. Scandals."
Christie's team is hitting back. In a speech Monday
, he pitched his experience as a prosecutor and governor to New Hampshire voters, and argued that challenging times call for "someone who has been held responsible and accountable for their decisions, not someone who just changes the next vote if the last one didn't work out." The address was a not-so-subtle dig at congressional rivals such as Rubio who, as Cruz is all too eager to remind people, changed his position on immigration reform.
Cruz vs. long shots
Mike Huckabee and Rick Santorum are hoping that strong showings in Iowa -- where they won the 2008 and 2012 caucuses, respectively -- will help sustain their campaigns.
And as they woo social conservatives and evangelicals in the Hawkeye State, they're taking aim at Cruz.
An ad from Santorum's campaign this week seeks to do this by contrasting the former Pennsylvania senator's tenure with Cruz's. A narrator recounts Santorum's achievements before cutting to video of Cruz reading "Green Eggs and Ham"
during his 2013 filibuster over Obamacare.
Huckabee's supporters, meanwhile, have adopted a sharper tone, with his super PAC, Pursuing America's Greatness, releasing an ad titled "Two Teds."
The attack attempts to paint Cruz as two-faced about his conservative values, using audio of Cruz at a New York City fundraiser saying that fighting gay marriage would not be a top priority of his administration.
The two Republicans' attempts to damage Cruz reflect their campaigns' understanding that their best bet at a long-shot run depends on a strong finish in Iowa -- and that Cruz's strength in Iowa makes that unlikely. Whether or not the attacks help Santorum or Huckabee, though, they could hurt Cruz enough to widen the lane for middle-tier candidates such as Rubio and Christie.
Trump remains on top
Meanwhile, Trump, who overwhelmingly leads the rest of the GOP field according to a CNN/ORC poll released late last month
, has received his share of flak from other candidates and the groups supporting them, even if they've failed to dent his seemingly impenetrable poll numbers.
The Kasich campaign and his super PAC, New Day for America, stepped up their attacks against Trump, releasing a TV spot last month mocking Trump's days peddling a name-brand steak line
. In November, the group released a spot effectively comparing Trump to Hitler and the Nazis
, and the PAC is spending $2.5 million in attack ads
against the real estate mogul in New Hampshire.
Meanwhile, the super PAC backing Jeb Bush, who has tried to position himself as an experienced alternative to Trump, called the real-estate mogul "reckless" and "impulsive"
in a 30-second spot last month. But Bush's efforts have had little effect, leading Trump to taunt him last week by saying he "wasted" $40 million
Trump himself has not issued any attack ads on TV, though he's gone after candidates
in short video clips on Instagram
. But the brash billionaire has vowed to return fire with a flurry of negative ads
if he comes under attack.