Washington (CNN) John McCain and Lindsey Graham sought Wednesday to balance their roles as Republican foreign policy hawks and the conscience of defense-focused conservatives with embracing areas where they agree with President Donald Trump, whom they've often sparred with in the past.

In a town hall hosted by CNN Wednesday night, the two heaped praise on Trump for his handling of North Korea and his tone in Trump's Tuesday night address to Congress, and said Trump might be a game-changer on immigration -- a figure influential enough with conservatives to achieve reforms that have eluded other presidents.

But they lambasted Trump over his approach to Russia -- which Graham called a "blind spot" -- and his calls for cuts to the nation's budget for foreign aid and diplomacy.

The two senators, typically simpatico on foreign policy, made clear that they will remain a thorn in Trump's side at times, despite being members of the same party.

McCain -- long labeled a "maverick" for bucking presidents of his own party -- said the two won't "go along to get along with any President."

"My biggest fear is not losing my job," Graham said. "My biggest fear is not standing up and speaking out when I know it's right."

Just 24 hours after Trump's first prime-time speech to a joint session of Congress, two lauded the President for his tone -- which McCain noted was a departure from Trump's warnings of "American carnage" in his inaugural address.

"I think he laid out a positive agenda, and frankly I think it was different from his inaugural address. And I think it was well-received by the American people," McCain told CNN chief political correspondent Dana Bash, who was moderating the discussion.

"We need more of that guy -- less of the tweeting guy," Graham said.

But the two also warned Trump against asserting that the raid in Yemen in which Navy SEAL William "Ryan" Owens was killed was successful -- despite a moving two-minute standing ovation for Owens' widow in which Trump declared his sacrifice "etched into eternity."

"Remember when we were told it's just a few dead-enders in Iraq? Remember when we were told, you know, ISIL's the JV team?" Graham said, pointing to foreign policy missteps by former presidents George W. Bush and Barack Obama. "Don't go down that road."

"Missions succeed and fail," McCain said. "But those who serve and sacrifice, that doesn't affect their courage and what they've done for our nation by putting themselves in harm's way."

The two said they are pleased that Trump plans to roll out a new version of his executive order banning travel from several majority Muslim countries -- this time excluding Iraq.

McCain said he was worried about "our interpreters, my friends, who literally put their lives on the line" in Iraq.

Graham said the initial travel ban was offensive to the 3,500 Muslims who serve in the US military.

"Here's what I hope the President understands: When you do something like this, if it's perceived as declaring war on the faith, we're all going to lose," Graham said.

On Russia

Graham said if the FBI determines Trump's campaign illegally coordinated with Russia, Attorney General Jeff Sessions "cannot make this decision" about whether to pursue prosecutions.

But he deflected a question about a new Washington Post report that Sessions twice spoke with the Russian ambassador to the United States during the 2016 presidential campaign, saying he needs to know more.

"If there were contacts between the Trump campaign and Russian officials, they may be legitimate; they may be OK. I want to know what happened between the Trump campaign, the Clinton campaign and the Russians," Graham said.

Both McCain and Graham lambasted Trump over his approach to Russia and the country's President, Vladimir Putin.

"When it comes to Russia, he has a blind spot. The bottom line is that Putin is disrupting democracy everywhere," Graham said.

McCain, who has called for a select committee to investigate Russia's attempts to influence the US election, said the country's efforts require more attention.

"Have no doubt, what the Russians tried to do to our election could have destroyed democracy," he said. "And that's why we've got to pay a hell of a lot more attention to the Russians and the things they're doing in Europe -- and right now, they're trying to determine the outcome of the French election, and they're using cyber."

On Trump's plans for Congress

While many of their Republican colleagues in Congress have worked to make inroads with the new administration, hoping to capitalize on GOP control over two branches of government, Graham and McCain have repeatedly broken with the White House.

The two criticized Trump over his calls to cut the budget for foreign aid through the State Department, saying that doing so would undercut the nation's efforts in the Middle East.

"You're never going to win this war through military force alone. The budget the President's proposing cuts the State Department by over 30%. That is soft power," Graham said.

He said the United States needs a budget for projects such as "building a small school" in combat regions like Iraq and Syria. "An education for a poor young girl is far more damaging than any bomb. That's got to be on the table," he said.

The two argued Congress can pass measures that reform the nation's immigration system, and Graham said Trump is well positioned to pressure conservatives to accept citizenship or some legal status for some immigrants.

"I think Trump has the ability to tell the right, 'You know, this is a good deal. Take it,'" Graham said.

Graham pointed to two questioners during the town hall -- one man whose son was killed by an undocumented immigrant and one young man whose mother was deported in January.

Turning to the young man, Graham said, "I can tell the difference between your mother and the person who killed his son. Don't you think most Americans can tell the difference?"

History with Trump

McCain and Graham are both unsuccessful former presidential candidates. McCain ran in 2000 and was the GOP nominee in 2008, while Graham was a member of the crowded Republican primary field in 2016 from which Trump emerged. The two are among the Senate's foremost national security hawks, and are typically in lockstep on foreign policy issues -- urging a larger US role in combating terror threats such as ISIS in Iraq and Syria and a tougher approach to Russia.

During the campaign, Trump feuded with both McCain, whose war-hero status he questioned, and Graham, whose personal cell phone number he read aloud while on national television.

And both have frequently criticized Trump during his five weeks in office.

In Munich on February, McCain fretted about "the growing inability, and even unwillingness, to separate truth from lies" -- a clear shot at Trump, who has espoused falsehoods about crowd size, voter fraud and more.

Graham, meanwhile, declared Trump's budget "dead on arrival" Tuesday, pointing to its cuts to the State Department and complaining that Trump didn't call for more significant increases in defense spending.

A lasting friendship

McCain and Graham both ended the town hall wiping away tears.

The moment came as the two leading Republican foreign policy hawks explained their close, years-long friendship.

"I feel like I'm on Oprah now," Graham joked.

Graham pointed to McCain's loyalty, saying the Arizona senator stuck with him through a tough GOP primary and during his presidential campaign, and has also supported fellow service members who, like McCain, were prisoners of war in Vietnam.

"He is loyal to his friends. He loves his country. And if he has to stand up to his party for his country, so be it," Graham said of McCain. "He would die for his country. I love him to death."

McCain said the two have "common ideals, common goals for our country."

But he also pointed to Graham's "humble" upbringing -- "including the fact that he raised his sister after his parents died. It's quite a great American success story."

McCain said their friendship began when Graham, then a House member, was presenting the House's case for impeachment of President Bill Clinton to senators. He recalled a Graham quip that came during a discussion of 2 a.m. White House phone calls to Monica Lewinsky amid fears she would take her affair with Clinton public.

"Congressman Graham, on the most solemn occasion, said, 'You know, where I come from, any man calling a woman at 2 a.m. is up to no good,'" McCain said. "I knew right then that Lindsey Graham was a guy I wanted to spend time with."