Pete Buttigieg likes to start off his stump speech by asking the crowd to envision the day when "the sun comes up" and Donald Trump is no longer president. The first potentially concrete development on this front takes place in two weeks, when Iowans go to caucus in the first Democratic voting contest on February 3.

He has been hitting the trail hard, reminding Iowa caucus goers that it is "decision time."

Four presidential contenders — Bernie Sanders, Elizabeth Warren, Amy Klobuchar and Michael Bennet — will be off the trail for most days over at least the next two weeks because they're sitting senators who are required to be present for President Trump's Senate impeachment trial. Though the trial has not yet begun, their obligations in Washington have already meant that Buttigieg has had Iowa to himself for a couple of days after the presidential debate last week.

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In that time, he's been giving some thought to his closing argument, about "why I'll be the right nominee to take on and defeat Donald Trump." He's leaning into moderation, presenting himself as an alternative to progressives Bernie Sanders and Elizabeth Warren, who are both polling strongly in Iowa. Where they focus on ideological purity, he's explaining "why I'm focused on bringing together, not just our party but our country when the time comes."

His stump speech revolves largely around faith, freedom and democracy. He's also consistent about stressing that his campaign aims to build a "sense of belonging," and he has a collection of anecdotes about how his campaign has emphasized that idea to its supporters.

A campaign aide told CBS News that the former South Bend mayor will continue to emphasize his belief in the importance of building a broad coalition. He often mentions his campaign is reaching out to the progressive wing of the Democratic Party, moderates and "future former Republicans."

The latest Des Moines Register/CNN poll showed that Buttigieg is third among likely Democratic caucus goers behind Bernie Sanders and Elizabeth Warren. The poll showed that 40% of Democrats in Iowa have decided who they will support, compared to 45% who said they can be persuaded to support another candidate.

At multiple campaign stops in Iowa, Buttigieg has acknowledged Iowa has a "thumb on the scale" in selecting the party's nominee — its winner has been the Democratic nominee 7 out of 10 times — but he also talks about how Iowa has been a leader in political and social issues that are personal to him.

"Iowa has a way of surprising America and leading it forward — 2008, Iowa made it possible for a candidate whose very name made his campaign extremely improbable to arrive on the scene as a front running presidential candidate and eventually president of the United States," Buttigieg said at a town hall in Mason City, of Barack Obama.

"About a decade ago, Iowa led the way in making it possible for a marriage like mine to exist," he noted. Iowa has recognized same-sex marriages since 2009.

Maryland Congressman Anthony Brown, who is a national campaign co-chair and the first Congressional Black Caucus (CBC) member to endorse Buttigieg, told CBS News in an interview that Buttigieg needs to convey his practical solutions to governing, his mayoral record, his military service and his faith in the final weeks to the caucus to convince undecided caucus goers.

"I think sharing his experiences, framing it in the values that we all share, demonstrating a strategic approach to our issues — I think that will set him apart from the other candidates," Brown added.

But some undecided voters who attended his events his past week still harbor misgivings about the 38-year-old candidate's experience.

"I think he needs to prove, other than say that 'it doesn't matter,' that he has the experience to lead," said Runal A. Patel, a 20-year-old college student who also volunteered for New Jersey Senator Cory Booker's presidential campaign. "I really hate that whenever he gets asked that question, he sort of just deflects and says, 'Well, you know the last president didn't have any experience.' I always think well, look how that presidency is going. You know, I don't think that that's a good answer."

Claire Schaefer, a 21-year-old college student whose first choice is Minnesota Senator Amy Klobuchar, also seems dubious that he has the experience to lead — or at least remains unconvinced by the argument he sometimes makes that experience doesn't matter so much. On the debate stage, he has argued that the decades of experience of his competitors have led the country nowhere.

"I guess in some ways his inexperience like makes me a little doubtful, and that's probably the only thing —and maybe his performance with voters of color," Schaefer said.

On the ground, national caucus director Travis Brock is planning to stay in Iowa until Caucus Day. While he usually splits his time between Nevada, which also holds a caucus, and Iowa, Brock recently embarked on a 19-stop tour around the state training volunteers and precinct captains across Iowa.

While Buttigieg held five events last Thursday, Brock spent nearly two hours training over 250 people in Polk County, the largest in the state. It's part of a broader effort to teach volunteers and caucus goers the delegate math and persuasion methods in order to convince undecided caucus goers.

Buttigieg is keenly aware that he'll need a strong finish in Iowa in order to build momentum heading into the other nominating contests.

"It continues to be the case that Iowa is very important because it's our opportunity to demonstrate our strength for a lot of voters who I think are very pragmatic in places like South Carolina and Nevada, who above all, want to see a candidate who can win," Buttigieg told reporters at a campaign stop in Nevada on January 11.