Heidi M. Przybyla

USA TODAY

The Orlando shooting is scrambling 2016 presidential election politics, but not necessarily in the way terrorism worries normally do.

Americans have historically favored Republicans to deal with terrorism threats, and Donald Trump is seeking to extend his party’s traditional advantage.

The real estate mogul is doubling down on a proposed temporary ban on Muslims and escalating his attacks on President Obama, even speculating that perhaps Obama doesn’t want to stop terrorism.

White House ignores Trump comments about Obama's motives

Alternatively, Hillary Clinton, who has called for national unity in the response to latest attack, potentially neutralized one of the Republican Party’s biggest talking points in criticizing the Obama administration by using the words “radical Islamism."

“By using that phrase she’s not going to be boxed in the way President Obama let himself be boxed in,” said Larry Sabato, director of the University of Virginia’s Center for Politics. In a Monday speech in Cleveland, Clinton also strongly reprimanded the Saudis and Kuwaitis for funding terrorism, a sign of her willingness to strike a more hawkish tone than she did in the Democratic primary.

Clinton calls for national unity in first speech since Orlando attack

Her response, particularly when compared to Trump's, may blunt any potential political advantage the presumptive GOP nominee may have otherwise gained, analysts said. The renewed emphasis on terrorism also highlights her record as the nation’s former top diplomat and as a U.S. senator from New York following the Sept. 11, 2001, terror attacks.

Trump, meanwhile, posted on Twitter that he appreciated "the congrats for being right on radical Islamic terrorism.”

“Nobody plays a good hand worse than Donald Trump,” said Sabato. “The fact that he would tweet out how this tragedy benefited him,” said Sabato, “it just tells you he has no real sense of what a president does and how a president does it,” he said. “It’s shocking really.”

The combination of Trump’s response and Clinton’s decision to distance herself from Obama may neutralize the Republican Party’s traditional political advantage in the aftermath of terrorism, said John Hudak, a senior fellow in governance studies at the Brookings Institution in Washington.

“This issue could cut both ways for the Trump campaign,” said Hudak. “Some will buy into his aggressive rhetoric on the issue favoring Muslim bans,” said Hudak. “For others, fear, worry, and skepticism about Trump's seriousness and readiness to lead may push people away from him.”

Clinton says the U.S.-led coalition in Syria and Iraq has made gains in the last month and that the U.S. should ramp up the air campaign and harden its defenses at home. She’s also calling for revisiting U.S. gun laws, including those that allow suspected terrorist sympathizers on the FBI’s no-fly list to legally purchase assault weapons.

In a Monday speech in Cleveland, she criticized the Saudis and Kuwaitis for allowing funding to flow to “radical” schools and mosques “that have set too many young people on a path toward extremism.” It was a stronger denunciation of Arab nations than she issued in the aftermath of the San Bernardino shootings in California during the heat of the Democratic primary.

FBI 'highly confident' Orlando killer was radicalized

Trump is pushing his Muslim ban, which he’d softened in recent weeks by calling it a “suggestion.” He’s also escalating his attacks on Obama, saying on NBC’s Today show, that maybe he “doesn’t want to get it.” In a later speech in Manchester, he accused Obama of handicapping the intelligence community and issuing visas to foreigners who mean Americans harm. He also said Clinton wanted to dramatically increase the number of Syrian refugees coming to the U.S.

“I refuse to be politically correct,” said Trump. “We need to tell the truth about radical Islam,” said Trump, “about how radical Islam is coming to our shores.”

John Brabender, a Republican strategist, said Trump is on “safe turf” in making the case that Obama is “incompetent” in the fight against terrorism and probably safe in revisiting his Muslim ban. Polls show a majority of Republicans support it.

“It is a political mistake to go so far as to suggest that President Obama does not want to stop the terrorists,” said Brabender, who was Rick Santorum’s senior strategist during his 2012 GOP campaign.

Trump seeks to make Orlando an election issue

George W. Bush won his 2004 re-election on terrorism worries in the years after the Sept. 11 attacks, and polls have historically shown Americans trust Republicans to handle the terrorist threat more than Democrats.

While Trump may not benefit politically the way Bush did, his response to the tragedy also probably hasn’t hurt him, the analysts agreed.

“Democrats believe this could be a turning point on the issue,” said Nathan Gonzales, editor of the nonpartisan Rothenberg & Gonzales Political Report. “The worst time to evaluate the politics of a tragedy is often in the immediate aftermath,” he said.

“I start as being skeptical that thing changed a lot of minds,” said Gonzales of the Orlando attack.