Washington (CNN) They are the dueling imps hovering over President Donald Trump's shoulders, whispering in his ear, cajoling, enticing, threatening as they stretch their president and their party in wildly divergent directions.

And incredibly, you can see the influences of Steve Bannon and Senate Majority Leader Mitch McConnell compete in the President's mind as he ping pongs between them. He has allegiances to both sides in this GOP civil war.

Tuesday night it was Steve Bannon, the former White House chief strategist who has declared a " season of war against a GOP establishment " and is targeting almost every incumbent Republican up for re-election in 2018.

Bannon was at the Arizona kickoff for Kelli Ward, who is challenging Trump critic Sen. Jeff Flake in the GOP primary, and taunted McConnell about the primary loss of one incumbent establishment Republican and the retirement of another.

"The last couple of days, Mitch has been saying this big thing, 'Hey, you gotta win, winners make policy, losers go home,'" Bannon said. "Hey Mitch! Note to self, Mitch, big Luther Strange (defeated in a special election primary) and little Bobby Corker (retiring) are both going home. These people, Mitch, it's 2-0, the people of Alabama and the people of Tennessee have already spoken. Your folks are going home, their folks are going to make policy. And guess what, Mitch. It's going to be the policy of the President of the United States Donald J. Trump, not what you want to do."

JUST WATCHED Bannon on Monday: It's a season of war against GOP Replay More Videos ... MUST WATCH Bannon on Monday: It's a season of war against GOP 01:11

Bannon's expert trolling was directed at McConnell, but it was during an appearance at the White House, standing next to Trump, that McConnell made the offending remarks.

What McConnell said is that Republicans have experimented with anti-establishment candidates in statewide contests for Senate seats in the past. It didn't go well. Here's that full McConnell answer, in which he ticks off a number of surprise primary winners from earlier elections:

"Look, you know, the goal here is to win elections in November. Back in 2010 and 2012, we nominated several candidates -- Christine O'Donnell, Sharron Angle, Todd Akin, Richard Mourdock. They're not in the Senate. And the reason for that was that they were not able to appeal to a broader electorate in the general election."

"My goal as the leader of the Republican Party in the Senate is to keep us in the majority. The way you do that is not complicated. You have to have nominate people who can actually win, because winners make policy and losers go home. We changed the business model in 2014; we nominated people who could win everywhere. We took the majority in the Senate. We had one skirmish in 2016; we kept the majority in the Senate. So our operating approach will be to support our incumbents and, in open seats, to seek to help nominate people who can actually win in November. That's my approach and that's the way you keep a governing majority."

JUST WATCHED Trump, McConnell: We have the same agenda Replay More Videos ... MUST WATCH Trump, McConnell: We have the same agenda 01:02

Trump came to Washington promising to stick his thumb in the eye of the establishment. But now that he's here, it's becoming clear that he needs it, at least up to a point, and that majorities are a big deal for any president, even this one, especially if he wants to accomplish anything on Capitol Hill in today's very partisan political environment. Even with their slim majority, however, Republicans have been able to move very little, or nothing, in the Senate.

Republicans have the benefit of defending few seats -- only nine of the 34 seats up in 2018. Democrats will need a political wave and a lot of luck in order to take the Senate.

But the importance of his majority, however slim and ineffectual, does seem to have penetrated Trump's outlook. Asked during that Monday appearance with McConnell if he supported Bannon's effort, Trump said he'd be talking to his former strategist.

"I have a very good relationship, as you know, with Steve Bannon," Trump said. "Steve has been a friend of mine for a long time. I like Steve a lot. Steve is doing what Steve thinks is the right thing. Some of the people that he may be looking at, I'm going to see if we talk him out of that, because, frankly, they're great people."

It's not clear if Trump has yet tried to talk Bannon out of his anti-incumbent quest, but Flake, the Republican senator Bannon was targeting Tuesday night, would probably not be one of those "great people" Trump now wants to protect. Flake recently wrote an entire book that, essentially, refutes Trumpism.

The President has been extremely critical of Flake on Twitter and also during a campaign appearance in Arizona. (Trump didn't take the opportunity to endorse Flake's challenger Ward when he traveled to the state in August, although he did huddle with potential Flake challengers during that trip ).

JUST WATCHED President Trump's full rally in Phoenix Replay More Videos ... MUST WATCH President Trump's full rally in Phoenix 01:15:47

Trump took McConnell's advice in Alabama, endorsing the more establishment choice, the appointed Sen. Luther Strange, who lost out to Roy Moore, the state judge who has said and continues to say extremely controversial things on social issues. CNN's Greg Krieg has chronicled some of the more incredible Moore moments . Bannon supported Moore and Trump clearly smarted at being on the wrong side of the ballot box.

He was asked Monday if he'd be OK with someone like Moore, who has said numerous inflammatory things about homosexuality, serving in the Senate. Trump dodged.

"I'm going to be meeting with Roy sometime next week, and we're going to talk to him about a lot of different things," Trump said. But I'll be meeting with him. He ran a very strong race. The people of Alabama, who I like very much and they like me very much, but they like Roy. And we'll be talking to him, and I can report to you then. OK?"

JUST WATCHED Anderson Cooper reads Trump's deleted tweets on Alabama special election primary Replay More Videos ... MUST WATCH Anderson Cooper reads Trump's deleted tweets on Alabama special election primary 02:35

The danger for Republicans is that in the December special election, Moore could lose a seat that would otherwise be a lock for Republicans. But that's a long shot. In Arizona, where Flake has shown the ability to win statewide and the 2018 election is expected to be close, victory for Ward in the primary could spell doom in November. Echo that situation in other purple states like Nevada, or in places where Democratic senators will have to fight hard for reelection, like Missouri. It was no mistake that McConnell mentioned Akin's 2012 race at the White House Wednesday. Akin flamed out after his controversial comments about " legitimate rape " caused an uproar and Democrat Claire McCaskill won what had been a hotly contested seat.

This is the push and pull of what's going on in Trump's mind.

On the one hand, Trump's standing next to McConnell, who needs that majority to do anything on Trump's punch list, saying his relationship with Republican senators is "fantastic." On the other, Trump has also very recently issued direct encouragement to those who would revolt against sitting Republicans.

Trump does appear to understand the need for Republicans to work in tandem since Democrats oppose his priorities in lock-step. But he has also directed his slings at McConnell, who couldn't come up with a simple majority of votes to repeal Obamacare. Trump has since sought to sabotage the law by cutting federal payments to insurers and rejected a bipartisan proposal to prop it up while Republicans think about a way forward.

The next test will be on an overhaul of the tax system, which Republicans have long wanted to accomplish. They're on course to do it by squeezing through Senate rules, sidestepping a Democratic filibuster and relying on a bare majority of Republican votes.

There's not unanimous support yet for the Republican tax plan, which is still a work in progress. Some Republicans have said the threat of Bannon's promised primaries could help get votes onboard for a party line tax reform vote, while others see Bannon's effort as counter-productive

"Just so you understand, the Republican Party is very, very unified," Trump said Monday, despite the civil war going on around him. He also said not to believe what you read in the news.

"I have a great relationship with political people," Trump said of the senators Bannon is targeting. "If you read the papers, you think -- I'm like on one island and they're like on the other. Well, it's not the way it is."