There's a vintage national security debate going on inside the Republican Party this Memorial Day over whether the US should go to war in Iraq.

The leading candidates don't want to box themselves in, but Bush-era neo-conservatives and a handful of the party's long-shot presidential candidates are pushing for a more robust US presence to combat the rise of ISIS. And that puts top Republican candidates in a tough spot between the party's national security base and a war-weary American public.

"Whatever one's judgment of Bush's policies, or Obama's, I hope this new debate on Iraq provokes a serious discussion of our policy options moving forward," Weekly Standard editor Bill Kristol, the heir to the original neo-cons, wrote in a USA Today op-ed last week. "If it does, I'm convinced Americans will come to the view that there's no alternative to American world leadership, and that such leadership must be backed by the threat of military strength and the willingness, in the right time and circumstances, to use it."

While the national security wing of the Republican Party has been obsessed with Iraq for a quarter of a century, regardless of the situation on the ground, the rise of ISIS, and the failure of the US-trained Iraqi army to fight effectively, may have made arguing for greater American engagement less politically radioactive than it would have been a year ago.

The sparse polling on adding combat troops in Iraq hasn't been consistent. A Rasmussen Reports survey released May 22 found that 35 percent of respondents backed a troop surge, compared with a high of 52 percent in a similar poll in February.

Still, if Kristol and his allies get their way — and it looks like they will — a willingness to insert thousands of American troops into Iraq will become a major debate point in the Republican presidential primary and the general election. Already, Senator Lindsay Graham of South Carolina, former Senator Rick Santorum of Pennsylvania, and former Governor George Pataki of New York have indicated their preference for beefing up America's physical presence in Iraq.

The challenge for many Republican candidates, as the New York Times pointed out Sunday, will be to embrace the principles of hawkish primary voters without trapping themselves into committing to a return of US forces that could prove unpopular by November 2016. That's why the saber-rattling hasn't been followed by forceful calls to put American troops in Iraq, particularly when it comes to candidates who have a real shot at winning the primary.

"I don’t think that will work," Jeb Bush told the Times of a possible US-led ground force in Iraq. But he has struggled to define his view of the American relationship with Iraq, at first stumbling over the question of whether he would have gone to war knowing what his brother knew at the time of the 2003 invasion.

His position now is a labyrinth: He wouldn't have gone to Iraq given what's currently known, the Obama administration made a mistake in withdrawing troops, and he thinks adding US forces would fail.

Senators Rand Paul of Kentucky and Ted Cruz of Texas, who are running for president, have been opposed to putting new American "boots on the ground" in Iraq.

"If the Iraqis are not willing to fight for their country, I don't think I would send more American GIs," Paul told CNN last week.

"Senator Paul believes in protecting American interests in the region, he's been supportive of air strikes since our consulate and embassy are under threat," his spokesman, Sergio Gor, told Vox. "However, Senator Paul also strongly believes that any action needs to be constitutional, and the first step would be passing an AUMF. He's introduced an authorization for use of military force in congress and hopes this administration will seek congressional authority. Finally, Senator Paul believes we need boots on the ground, but those boots ought to belong to Saudi, Qatari, Kuwaiti among other local participants."

So while the Democratic Party seems united in its wariness of a large-scale return to Iraq, Republicans have an intraparty fight brewing. Some believe the winning formula both for the primary and the general election is an emphasis on the national security approach favored by President George W. Bush. The battle over the extension of Patriot Act provisions that form the basis of the National Security Agency's bulk data collection program is another front in the same fight for the soul not only of the Republican Party but for control of the nation's counterterrorism and foreign policy agenda.

"There is no role whatsoever for American soldiers"

On the Democratic side, 2016 frontrunner Hillary Clinton drew a line in the sand, so to speak, on Friday.

"American air support is available, American intelligence and surveillance is available, American trainers are trying to undo the damage that was done to the Iraqi army by former Prime Minister Maliki, who bears a very big part of the responsibility for what is happening inside Iraq today," she said. "But at the end of the thought process that I engage in ... this has to be fought by and won by the Iraqis. There is no role whatsoever for American soldiers on the ground to go back other than in the capacity as trainers and advisers."

That's closer in line with President Barack Obama's policy than many Democrats would have expected from Clinton, who pointed last year to Obama's decision not to arm Syrian rebels as the proximate cause of the birth of ISIS.

"We are losing. There's no doubt about it." — Former US Ambassador to the UN John Bolton

The argument for being ready to significantly increase US troop presence in Iraq, pushed by former Bush administration officials and conservative thinkers, rests on the conclusion that ISIS is an outsize threat to American national security and that its gains of turf and strength have weakened the US.

That view is certain to be aired more frequently and with greater ardor in the wake of the ISIS victory in Ramadi and Defense Secretary Ash Carter's acknowledgment in an interview with CNN that Iraqi soldiers had "no will to fight" in that battle.

Lightning Bolton

"I think [the White House has] been in denial about the war on terror for the last six-plus years. They don't want to admit we're in a war. They'd rather treat it as a law enforcement matter," John Bolton, the former US Ambassador to the UN under Bush, said on Fox News Sunday. "That's palpably wrong. I think their unwillingness to understand the nature of the ideological threats we face from the likes of ISIS paralyzes them in ability to deal with it effectively. And we are losing. There is no doubt about it."

Bolton said he isn't running for president but wants to try to steer the debate toward a more aggressive US response to ISIS.

"I think that Turkey and the Arab states nearby have a huge stake in working with us to destroy ISIS before it really consolidates its control over the territory it holds, rips up the post-World War I map of the Middle East, and creates a new state, which is its objective," he said. "Those Arab forces and the Turks can't do it alone. They need American leadership. They need us there with them. It's wrong to say it's their problem, let them handle it. Are we really saying we're going to put American security in the hands of the Saudi defense ministry? I don't think so. What I've said is very unpleasant to hear. Politicians shy away from it. I think it's inevitable."

Pataki called for the insertion of troops last week on CNN.

"I don't want to see us putting in a million soldiers, spend 10 years, a trillion dollars, trying to create a democracy where one hasn't existed," he said. "But send in troops, destroy their training centers, destroy their recruitment centers, destroy the area where they are looking to plan to attack us here, and then get out."

While Bush shied away from advocating for a troop increase in the Times interview, he recently told a college student that drawing down over the last few years gave ISIS the oxygen it needed to grow.

"Look, you can rewrite history all you want, but the simple fact is that we’re in a much more unstable place because America pulled back," he said.

"Our military is too good for that"

However, it's not a settled matter within the Republican Party. Last year, Kentucky Senator Rand Paul wrote an op-ed in Politico criticizing former Texas Governor Rick Perry for mischaracterizing Paul's politics and wanting to put more US troops in Iraq.

"Unlike Perry, I oppose sending American troops back into Iraq. After a decade of the United States training Iraq’s military, when confronted by the enemy, the Iraqis dropped their weapons, shed their uniforms and hid. Our soldiers’ hard work and sacrifice should be worth more than that. Our military is too good for that," Paul wrote.

There's a "significant difference between 150,000 US troops and 10,000." — White House Press Secretary Josh Earnest

The Obama White House remains resolute in its opposition to radically bolstering the American force in Iraq, but has left the door open to a more limited scaling up of troop levels.

"The president has made very clear that he does not envision a scenario where we commit hundreds of thousands of US troops to a sustained ground combat operation inside of Iraq," White House Press Secretary Josh Earnest said May 19. "That would clearly not be in the best interests of the United States, and it’s not something that the president would consider. And incidentally, it’s also not something that the president’s military advisers have recommended at this point."

But in the same exchange, Earnest pointedly declined to answer whether Obama is considering a smaller troop increase of 10,000, calling it a "hypothetical thing." And he hastened to "highlight the significant difference between 150,000 US troops and 10,000."

After America made a mess in Iraq — sacrificing more than 4,000 US troops and more than $800 billion for no discernible victory other than the removal of Hussein — some believe only America can fix it.

The debate is likely to continue deep into the 2016 presidential contest, as long as neither Iraqi nor US forces can repel ISIS. Going to war in Iraq didn't feature in the presidential contests before the 1991 and 2003 US wars there because it wasn't on the radar at the time of the elections. Now Americans will get to listen to the arguments for and against going into Iraq as they choose their next president.