McCain: GOP Fighting While Obama 'Puts Us in More Jeopardy'

"It seems to me the lesson we should have is to sit down together and come up with a common agenda, and have our differences but please don't disparage each other's characters, integrity and motives."

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McCain said he considers Boehner a "fine man" who has had a "very difficult job in his leadership role," and now he would like to speak with House Republicans about the importance of getting along and getting a Republican president elected.

"It's time we had a dialogue rather than continuing to disparage each other's character, calling the majority leader a liar," said McCain of Republicans in both Congressional chambers, referring to Sen. Ted Cruz' comments to Senate Majority Leader Mitch McConnell earlier this summer. 

But unlike in the House, McCain said, there is "no sentiment here amongst the overwhelming majority of my Republican colleagues in the Senate to replace Mitch Mcconnell. We appreciate his leadership and there's no chance of that happening."

Political infighting, continued McCain, are a detriment and "very unhealthy" to the party of Abraham Lincoln and Ronald Reagan, McCain told the Morning Joe program.

And while the political fighting is going on, there is "no strategy" to fight ISIS and "we are surprised when [Russian President] Vladimir Putin exercises what is a very clear strategy, and that is to increase his influence in the region, said McCain, pointing out that Putin wants to ensure that Syrian President Bashar al Assad or an easily controllable protege stays in power.

The veteran senator also appeared on Fox News' "America's Newsroom," where he complained that Putin "played the United States like a Stradivarius," as this country "has no strategy or plans besides airstrikes, which have clearly been ineffectual."

There is a vacuum created by the United States' withdrawal from Iraq, said McCain, and that has resulted in Arab countries collaborating with Russia and Iraq's announcement that it will share intelligence with Russia, Iran, and Syria about the Islamic State.

McCain told Fox News' Bill Hemmer that Ukraine is "very nervous" about Obama's planned talk with Putin later in Monday, as that country's government is worried if Obama is "going to throw them under the bus and basically acknowledge the dismemberment of that country Putin has been responsible for?"

He said he is not against Obama speaking with Putin, "but when the Secretary of State [John Kerry] calls the foreign minister of Russia three times to try to find out what Russia is doing, what kind of leadership role is that?"