Washington (CNN) Discussions about North Korea, a meeting between President Donald Trump and Russian President Vladimir Putin, and the future of the Supreme Court dominated Sunday morning's political shows this week. Trump's lawyer, Rudy Giuliani, also managed to make it onto three of the shows, where he repeatedly addressed issues surrounding Trump's former personal attorney Michael Cohen and the potential for an interview between the President and special counsel Robert Mueller.

The Trump-Putin meeting

Trump plans to meet one-on-one with Putin at the start of their July 16 summit in Helsinki, Finland, according to a person familiar with the plans. The meeting will be the first formal summit talks between them.

on NBC's "Meet the Press" said he doesn't think there's anything wrong with talking to the Russians." "There's nothing wrong with the President talking to Putin. There's nothing wrong with my colleagues talking to the Russians, but you've just got to understand who you're talking to," he remarked.

Iowa Republican Sen. Joni Ernst spoke to CBS's "Face the Nation" about a recent White House proposal to work with Russia in Syria. Ernst said she "would just caution the President as we move forward with any discussions with Russia. Obviously, Russia is not our friend. ... I don't see that Russia would ever be a true friend or ally to the United States."

On CNN's "State of the Union," Sen. Jeff Flake, R-Arizona, told Dana Bash that "many of us are concerned" when Trump "ridicules our allies and praises our adversaries."

JUST WATCHED Flake: Concerned what Trump could promise Putin Replay More Videos ... MUST WATCH Flake: Concerned what Trump could promise Putin 00:43

Flake said that if he could advise Trump on what to say to Putin, he would say "One, that annexation of Crimea will not stand. We cannot accept that. Two their involvement in ... eastern Ukraine is not going to be accepted. And the sanctions will continue until the behavior stops and that we know that Russia ... interfered with our elections."

Giuliani said on said on "Meet the Press" that Trump "has to sit down with Vladimir Putin. ... Putin's going to have to meet him more than halfway."

The US plan to denuclearize North Korea

Secretary of State Mike Pompeo traveled to Pyongyang over the weekend to hold more talks with North Korea regarding denuclearization. Pompeo hailed the negotiations as "productive." North Korea, however, poured cold water on the talks, saying the "attitude" of the US was "regrettable" and not in the spirit of the June 12 summit in Singapore between Trump and North Korean leader Kim Jong Un.

South Carolina GOP Sen. Lindsey Graham told "Fox News Sunday" that "there's no doubt in my mind that it's the Chinese pulling the North Koreans back. And to our North Korean friends, can't say the word friend yet, you asked Pompeo, did he sleep well? If you knew what I knew about what we could do to the leadership of North Korea, you wouldn't sleep very well."

Blunt told "Meet the Press" that nobody should be surprised by North Korea's "foot dragging" over denuclearization. "Apparently, it's not what they meant to say when they said it," he said, later adding that "we're going to denuke North Korea. It's going to start immediately." He also said that he thought the halt of military exercises with South Korea was "a mistake."

Ernst said on CBS that she thought the US-North Korea talks were a mark of progress toward denuclearization, but added that military exercises should commence "soon if we don't see those talks continue."

Democratic Sen. Chris Coons, of Delaware, told "Face the Nation" that there haven't been many developments on a detailed strategy for achieving the agreement made in Singapore last month.

"I commend Secretary Pompeo for how hard he's trying to make something out of nothing, but so far I don't see that we've accomplished much, and my concern is that President Trump unilaterally gave away doing military exercises with our vital allies -- South Korea and Japan -- without consulting with them, and we got nothing but empty promises of denuclearization from Kim Jong Un," Coons said.

On CNN's "State of the Union," Flake said it seems "par for the course" for Pyongyang to rebuke Pompeo's efforts in North Korea.

Mueller's interview with Trump

Giuliani confirmed on "State of the Union" that the White House contested a request from the special counsel to interview White House chief of staff John Kelly.

Giuliani also spoke about the latest preconditions he is demanding for an interview between the special counsel and Trump.

Asked about a report in The New York Times that included news of the pushback against Mueller's request for an interview with Kelly, Giuliani said the special counsel team was dealing with White House attorney Emmet Flood on that issue.

"I'm glad to see that Emmet is using a high standard because after all, we've given them everything they ask," Giuliani said. "Thirty-two witnesses, no invocation of privilege. 1.4 million documents, no invocation of privilege. Tell me we have something to hide. We have nothing to hide."

Cohen's potential 'flip'

And last week, Cohen suggested during an interview with ABC News that his loyalties have shifted away from Trump.

Giuliani that he isn't concerned about Michael Cohen potentially cooperating with federal prosecutors. said on "State of the Union" that he isn't concerned about Michael Cohen potentially cooperating with federal prosecutors.

"I don't know what he has to flip over," Giuliani said of Cohen. "What I do know is there is no evidence of wrongdoing with President Trump. So we're very comfortable. If he believes it's in his best interest to cooperate, God bless him. He should cooperate. I think the man has been horribly treated by the people he's going to cooperate with, but sometimes you have no other choice."

He also told ABC News' "This Week" that there has not been a discussion with Trump about pardoning Cohen.

Trump's SCOTUS pick

Trump told reporters last week that he had interviewed four candidates to replace retiring Supreme Court Justice Anthony Kennedy, signaling an aggressive push toward picking a nominee by his self-imposed deadline of July 9.

Alabama Democratic Sen. Doug Jones said on "State of the Union" that he's open to voting either way on Trump's pick. "I'm open to voting yes. I'm open to voting no. We don't know who the nominee is going to be yet," Jones said.

JUST WATCHED Jones: Delaying SCOTUS vote 'not going to work' Replay More Videos ... MUST WATCH Jones: Delaying SCOTUS vote 'not going to work' 02:44

Coons conceded on CBS that "if all the Republicans stick together, along with the vice president, they'll be able to confirm whomever President Trump nominates."

Senate Minority Whip Dick Durbin told "Meet the Press" that Senate Majority Leader Mitch McConnell's decisions to delay the consideration of President Barack Obama's nomination of Merrick Garland to the Supreme Court until after the 2016 election, but not to do the same thing time around, are "either wrong the first time or wrong the second time. The net result is he's trying to play to his political advantage."

Blunt also said on "Meet the Press" that the Senate "can confirm any of the four names being mentioned. There are reasons to look at both the Pennsylvania and the Michigan nominee."

Leonard Leo, who heads the Federalist Society and helped craft a short list for Kennedy's replacement, acknowledged McConnell's assertion last week that two candidates on the list, Ray Kethledge and Tom Hardiman, would have more difficulty getting confirmed.

"They're a little less known by conservatives and their records are a little lighter so it might take some time," he told "This Week."

The future of NATO

Flake said on CNN that NATO allies "are very concerned about what they hear" in Trump's rhetoric. "I'm glad that the President is raising this issue with NATO countries. Many of them are not pulling their full weight. But the President makes it sound as if they're supposed to contribute 2% to the US somehow for their defense," he added.

JUST WATCHED Flake: NATO allies have a reason to be concerned Replay More Videos ... MUST WATCH Flake: NATO allies have a reason to be concerned 02:33

NATO Ambassador Kay Bailey Hutchison said on said on "Fox News Sunday" that the organization "really is making progress and they are doing it really at President Trump's insistence."

Democrats on immigration

The Trump administration has faced mounting criticism from Democrats and immigrant advocates for separating children from their parents once families are apprehended at the US Mexico border.

Durbin dismissed dismissed recent pushback from the Trump administration suggesting that there were not enough resources for dealing with undocumented immigrants being held in overcrowded detention centers.

"I can tell you they have the resources to get it done, Chuck," Durbin told "Meet the Press" host Chuck Todd. "This is not an accident. This is a policy of deterrence, to stop the future flow, to be mean to these kids and their families, to say to others, 'Don't even try it.' That, to me is cruel. That's not what America is about."

Jones rebuffed a call from fellow Democrats to abolish US Immigration and Customs Enforcement (ICE), which has become more prevalent among Democratic lawmakers in the wake of the family separation crisis.

"I'm not in favor of abolishing ICE. We've got to have government operations that will enforce our immigration laws, even though the immigration laws need an overhaul," Jones told "State of the Union. "The problem with ICE right now is not the boots on the ground or the folks doing the enforcement. It's the orders that are coming down to those folks on the ground."