Washington (CNN) President Trump's big challenges at the United Nations, the spotlight on his ambassador and new wrinkles in two big Senate races filled our Sunday trip around the "Inside Politics" table.

1) Refugee policy a big tug-of-war inside team Trump

Among the many questions facing the Trump administration at the President's first United Nations General Assembly is how many refugees it will allow to enter the United States.

Candidate Trump promised to roll back Obama administration policies, and some conservative voices in the White House are pushing to set an annual entry number below 50,000. But more moderate voices in the White House are urging the President to be more welcoming. Julie Hirschfeld Davis of The New York Times shared reporting on the back and forth and how it impacts the President's dealings with other world leaders at the UN gathering.

"There was a meeting last week at the White House," Davis said, referring to the refugee issue. "There's still a lot of disagreement, the Defense Department, the State Department, US, UN, they're all pushing back against this notion of less than 50,000 refugees coming into the United States next year, but what we're seeing is that there's still a hard line stream within the White House, Steve Miller, some of the other aides that have been driving this discussion, that are really getting in the President's ear about this. And they're able to keep this notion alive."

2) Iran policy another giant question

Another giant global question facing Trump is whether to stop certifying Iran as being in compliance with the nuclear deal negotiated by the Obama administration -- and his speech and meetings at the United Nations this week could offer some clues.

The President often criticizes the deal, but his administration so far has deemed Iran to be in compliance. Whether it will do so again at the next deadline is the big question -- so the President's words when he speaks at the General Assembly, and when he meets with Israeli Prime Minister Benjamin Netanyahu, will be closely watched for hints.

It isn't just the other world leaders who are eager to know if a big shift is coming. Karoun Demirjian of The Washington Post has been speaking to key members of Congress -- who will be forced to confront the Iran compliance question if the President shifts course.

"This is making everybody a little bit nervous right now, it's making members of Congress nervous," Demirjian said. "We saw that this morning, the Ayatollah was tweeting up a storm about the US and the Iran deal in ways that are not, you know, an everyday occurrence."

"If he decides not to certify the sanctions, that kicks things back to Congress where people are not saying what they think the President will do, but are making contingency plans or taking steps to get ready," Demirjian said. "Because if that happens, they're going to have about 60 days in which to decide whether or not to blow up that deal."

3) Haley also in UN spotlight; some see it as a prelude

Nikki Haley is guaranteed a place in the spotlight this week by the nature of her job as US ambassador to the UN. But there is more to it than that, because of questions about the man who is, on paper anyway, her boss: Secretary of State Rex Tillerson.

Talk of a "Rexit" has calmed a bit in recent weeks, but it is no secret that Tillerson has felt deep frustration with the White House.

Politico's Eliana Johnson also notes that Tillerson keeps a much lower profile than many who have served as America's top diplomat, and that talk of Haley eventually stepping into that role is a big subplot as the President and his team attend their first UNGA.

"I think she's sort of served as a shadow secretary of state," Johnson said, "because Secretary of State Rex Tillerson hasn't embraced the public aspects of the job that we've seen typical secretary of states do, and they haven't always spoken in a unified voice."

"It seems almost conventional wisdom that she may succeed Tillerson, who's not expected to stay longer than one or two years," Johnson added.

4) Arizona race may get another Democratic candidate

Arizona GOP Sen. Jeff Flake is persona non grata to President Trump, and a target of anti-establishment GOP forces like Breitbart and its chief, former White House chief strategist Stephen Bannon.

That particular 2018 Senate race drama -- in which the incumbent Republican president is urging the primary defeat of an incumbent Republican senator -- often overshadows a crowded race on the Democratic side to pick a Flake challenger. And CNN's Nia-Malika Henderson told us the Democratic field may get another addition: Rep. Kyrsten Sinema.

"Somebody who's going to be interesting to watch over these next couple of weeks is Kyrsten Sinema," Henderson said. "She was one of the handful of House Democrats to meet with President Trump over these last weeks, talking about tax reform, DACA, infrastructure, she is very much a blue dog Democrat."

"Should she get in (the Senate race), it will be a referendum again on is the Democratic party more centrist or is it more progressive in sort of the Bernie Sanders mold."

5) At odds in DC, but Trump and McConnell are 'Strange' bedfellows in Alabama

Add this to a rather confusing week of odd and shifting allegiances in Washington: President Trump is heading to Alabama, hoping to help Senate Majority Leader Mitch McConnell. Yes, the same Mitch McConnell he has publicly criticized for failing to get Obamacare repealed and failing to get other GOP agenda items through Congress.

The President announced on Twitter he will head to Alabama this coming weekend to campaign for interim GOP Sen. Luther Strange, who is running behind with little more than a week to go in the state's GOP Senate runoff.

Now Trump endorsed Strange weeks ago, so that's no big deal.

But he has been silent about the race in recent weeks as Strange has fallen behind former Alabama Supreme Court Chief Justice Roy Moore, and until Saturday's tweet had been noncommittal when asked if he was willing to put his personal prestige on the line in the race's final days.

Now, his decision made, the President is, if you will excuse the cliché, making a "Stange" bedfellow with McConnell.

Think about it: President Trump is making a high profile late campaign trip to help McConnell and the GOP establishment. And that trip puts him directly at odds with Christian conservatives and anti-establishment GOP forces including his former top White House strategist Bannon.

The race has become, for the most part, a referendum on McConnell and the GOP establishment, but with his late play, the President is also making it a test of his standing with GOP voters.