WASHINGTON — The two people most frequently mentioned to head the Pentagon in Donald Trump’s administration are both senators — and some of their chamber’s most hawkish Republicans.

They are Alabama’s Jeff Sessions — one of Trump’s closest allies and a top booster since the start of the businessman’s unconventional campaign — and Arkansas’s Tom Cotton, an Iraq and Afganistan Army veteran and at 39, the youngest member of the Senate.

Their colleagues are, at this point, used to their often controversial stances on national security, such as Cotton’s recent argument that waterboarding isn’t torture. Sessions also recently voted against anti-torture legislation, which puts both in line with Trump, who backs the use of waterboarding and “much worse” as interrogation techniques.

But if Trump goes with Sessions, Washington Republicans could be in for a rude awakening: the Alabama Republican has long campaigned for smaller federal budgets, and doggedly favors keeping as a ceiling the overall budget caps that Congress almost surely must lift in order to approve the dramatic defense ramp-up that Trump promised during his campaign.

Defense hawks in Congress are certain that with Cotton, they could raise spending to the levels they have been clamoring for. With Sessions, they aren’t quite so sure.

“Tom Cotton is all in for more defense spending,” Sen. Lindsey Graham, R-S.C., who said he would vote for either pick, told reporters Tuesday. “Jeff Sessions I think supports more defense spending but he’s been more of a deficit hawk.”

“I have no thoughts about any of the appointees of the president, that’s his prerogative,” commented Senate Armed Services Committee Chairman John McCain, R-Ariz.

But the Pentagon’s new head may well come from McCain’s rank-and-file. If that happens, the move would not be unprecedented: former president Bill Clinton’s defense secretary William Cohen, R-Maine, served on that panel before joining the administration, and Obama Pentagon chief Chuck Hagel, R-Neb., had served on Senate Foreign Relations.

Both Sessions and Cotton are Armed Services members. Sessions, who will turn 70 next month, has far more seniority than Cotton, who at 39 would be one of the youngest-ever Secretaries of Defense if selected.

Both have military experience, though Cotton’s is more recent and perhaps more relevant: He spent four years on active duty, the bulk of it in the Army’s 101st Airborne Division, which included seeing combat during deployments to Iraq and Afghanistan, before joining the Army Reserve for another four years. Sessions was in the Army Reserve from 1973 to 1986.

But neither of the two has significant executive experience running an operation anywhere near as large as the Pentagon, where they would be in charge of over 25,000 employees on-site, not to mention the nearly 2 million additional members of the armed services and reserves, and a budget that constitutes about a sixth of all federal spending.

The next secretary of defense will have to manage that massive operation during a period of significant changes, as Trump and his advisers have promised a massive spike in military spending.

They propose a significant increase in the size of the Army, going from about 450,000 to 550,000, close Trump confidant Rudy Giuliani said over the weekend. They also want a hike in the number of naval warships to 350, from the approximately 275 currently in service. Trump pledges to invest more in cyber defenses, and GOP leaders are looking to him to modernize the nuclear arsenal and pursue a massive expansion of missile defense. Not to mention pay for keeping up the fight against the Islamic State and other radical groups abroad.

In either candidate, Trump would inherit one of the Senate GOP’s most unabashed iconoclasts: both have, with varying degrees of success, been more than willing to vote and embrace hawkish stances that Democrats and even some Republicans have criticized as extreme. Both, for example, are opposed to women serving in infantry roles, and recent efforts to require women to register for the Selective Service.

Cotton made a name for himself soon after arriving in Washington by penning a letter to the Ayatollah of Iran disputing the Obama administration’s right to engage in negotiations over the Iran nuclear deal — a deal Trump has called “terrible” — and pulling almost all Senate Republicans on board. Sessions, meanwhile, is renowned for being one of Congress’s most uncompromising voices on immigration enforcement, which fits in well with the president-elect’s plans to build a southern border wall.

Both Cotton and Sessions believe that the United States should have kept more troops in Iraq, and agree with Trump that waterboarding should an available tool to U.S. interrogators — Cotton recently went so far as to argue that waterboarding doesn’t constitute torture — a stance considerably more hawkish than that held by most members of Congress.

But when it comes to the defense budget, there are key differences. Cotton’s position is fairly mainstream for the GOP: He wants a full repeal of the budget caps imposed under the Budget Control Act, and a shift of resources toward defense spending — the current defense budget, he said last year, represents what “is necessary, but it’s not sufficient.”

Sessions, meanwhile, comes from the school of deficit hawks who believe that the budget, even capped as it is, may already be too large.

Sessions’s and Cotton’s office did not respond to requests to comment for this story, but fellow Alabama Republican and Sessions friend Mo Brooks agreed with the idea that any increased money for defense should be compensated for elsewhere in the budget.

“We should not spend more money on national defense if the source of that money is increased borrowing,” Brooks saidm expressing confidence that Sessions would agree. “We have to offset all reallocation of priorities based on spending cuts from other parts of the federal government that are a lesser priority.”

To Brooks, that means making draconian cuts to programs like welfare and foreign aid — proposals that are likely to draw a backlash from Senate Democrats able to block action. They would encounter opposition from even some Republicans, such as Graham, who has advocated a new “Marshall Plan” for the Middle East as an integral part of the fight against terrorism.

In the Senate, Sessions’s voting record sheds some light on his approach to defense dollars: He votes for the annual defense policy bills, but often votes against additional emergency spending measures that fund military operations in Afghanistan and the Middle East. In 2014, Sessions was one of only three senators to vote against a bill to fix health care delays for veterans, expressing fears about the cost.

At this point, defense leaders in Congress have no clear indication from the Trump transition team about whether or how they will try to lift the defense budget caps. Their pick for Pentagon chief could foreshadow the direction in which the Trump administration will lean.

“I hope we do lift it,” House Armed Services Chairman Mac Thornberry, R-Texas, said of the defense sequester Monday, though he added: “I haven’t talked to him,” meaning Trump, about his plans.