First lady Michelle Obama campaigned for Democratic presidential nominee Hillary Clinton in Phoenix, taking aim at Donald Trump by saying, "He just doesn't understand us." (Victoria Walker/The Washington Post)

A year ago, few who have watched first lady Michelle Obama only reluctantly participate in the rough-and-tumble of campaigning would have predicted that she might emerge in this election’s final weeks as Hillary Clinton’s most potent surrogate.

But after a rousing speech last week in New Hampshire in which she passionately renounced Republican Donald Trump, and another in Arizona on Thursday making the case for Clinton’s vision for the presidency, Obama has demonstrated an ability to do what Clinton herself has struggled with for much of her campaign: explain why voters should vote for her.

“Do not let yourself get tired or frustrated or disgusted by everything you’ve seen in this campaign. Please, be encouraged,” Obama told a crowd of about 7,000. “I have traveled the world, and I am telling you we still live in the greatest country on Earth. We have every reason to be hopeful. Remember that in difficult times, we don’t give up. We don’t discard our highest ideals. No! We rise up to meet them. We rise up to perfect our union. That is the power of hope!”

The first lady has shown a willingness to pitch in wherever Clinton needs her — including a speech in the traditionally red state of Arizona, where Obama’s appearance reflected the campaign’s growing ambitions for a landslide victory on Nov. 8.

First lady Michelle Obama responded to Donald Trump for refusing to say whether he’ll accept the presidential election results during the final presidential debate in Las Vegas. (The Washington Post)

Clinton has embraced Obama’s role on the campaign trail — and has long expected her to play an important role in the election’s final weeks, said Jennifer Palmieri, the candidate’s communications director. The fact that Clinton is contesting Arizona — and believes that the African American wife of the nation’s first black president is an effective emissary to a deep-red state — reflects how important she is to the campaign, Palmieri said.

“There is just not anyone more effective than her,” Palmieri said. “And as someone who doesn’t do a lot of politics, she has a lot of credibility when she does speak and when she does choose to get involved.”

The first lady first made headlines on the campaign trail this year at the Democratic National Convention, where she decried what the nation’s children might be learning from Trump’s coarse words. Last week in New Hampshire, she again played the role of the nation’s moral authority, imploring voters, out of a sense of decency, to deny Trump the presidency following revelations of his lewd descriptions of unwanted sexual advances.

On Thursday, Obama pivoted to a more positive subject: giving voters a reason to turn out for Clinton by laying out her vision for the presidency and the country — though not without throwing a few barbs for Trump.

She described Trump’s vision for the country as one of “hopelessness and despair,” “riven by division and ruled by fear,” and Clinton’s as one of “inclusion, equality and equal justice for all.”

“She has the policies to actually make that vision a reality,” Obama added, referring to Clinton’s plans to make college more affordable, increase the minimum wage and overhaul the nation’s immigration laws.

Last week’s speech about Trump’s lewd behavior would have been harder for Clinton, who is mistrusted by nearly as many voters as Trump. And on Thursday, Obama explained what kind of president Clinton would be in a way that Clinton has rarely achieved.

All of it reveals another side to the first lady’s role as surrogate: In some ways, she is a reminder of Clinton’s weaknesses and of how much less popular and compelling the candidate is among voters.

Michelle Obama is more popular than her husband, both presidential candidates and both political parties. According to an NBC-Wall Street Journal poll published this week, she is liked by nearly 60 percent of Americans.

Obama’s time, which she fiercely protects, is a coveted commodity. The Clinton campaign sees her as unique among their high-profile surrogates because of her ability to simultaneously appeal to voters who need to be persuaded to vote for Clinton and to voters in Clinton’s base.

The campaign has not decided where to deploy Obama next, but they are looking to send her to other expansion states as well as more traditional battlegrounds, Palmieri said. However, while Palmieri conceded that Clinton is not seen as being outside the political system like Michelle Obama, she did not directly acknowledge that Obama can deliver a message that Clinton cannot.

“She’s not a part of the horse race; she’s not part of the game,” Palmieri said of the first lady. “She is not involved in the day-to-day back-and-forth of the campaign. So when she speaks out, she brings a lot of clarity.”

Thursday’s speech came at a time when Obama knew that her words would draw national attention. Her raw and emotional indictment of Trump, whom she described last week as a sexual predator following the release of tapes where he bragged about assaulting women, reverberated across the country for days.

She has been intimately involved in drafting her remarks. “These are very much her messages,” one of the first lady’s aides said. “No one is coming to her and telling her what she needs to say.”

In her speech Thursday, Obama repeated her assessment that Trump’s words degraded all women and “decent” men.

She also rebuked Trump for promising to keep the country “in suspense” as to whether he would accept the results of the election.

“You do not keep American democracy ‘in suspense,’ ” Obama said, using air quotes to mock the Republican candidate.

But the primary focus of her speech was a nostalgic harking-back to her husband’s first campaign for president, when his campaign slogan was “Yes, We Can!” and his placards carried the words “Hope” and“Change.”

“Who are we?” Obama asked. “We are a nation founded as a rebuke to tyranny. . . . We are a nation that said, ‘Give us your tired, your poor, your huddled masses.’ ”

Obama is among several surrogates, including Sen. Bernie Sanders of Vermont and Chelsea Clinton, who have come to Arizona to rally voters for Clinton in recent days, giving Democrats here hope that the state will tip their way in a presidential election for the first time since 1996, when Bill Clinton won here. The campaign has 32 offices and 160 staffers on the ground in Arizona as part of a coordinated campaign with state, local and national Democrats. And this week, Hillary Clinton’s campaign manager, Robby Mook, announced that more resources are coming.

Obama’s popularity is buttressed by the long goodbye the nation has begun with her family. She fit the campaign rally in between her and her husband’s final state dinner and a White House music event they are hosting Friday with Black Entertainment Television. Photos of the first lady in the rose gold Atelier Versace dress she wore to the dinner were a point of conversation on social media when she landed here.

Democrats, including Clinton, often quote the Obama family’s motto, “When they go low, we go high.” Clinton gives credit to her “friend” Obama, linking herself to the first lady’s promotion of wholesome family values.

Obama seemed to relish her time before the audience here. Several people yelled, “We love you Michelle!” She came to the national scene nine years ago with an aura of accessibility fueled by jokes about the Barack Obama she knew — a man with morning breath and an annoying snore. In some corners, her edginess brought on accusations of being angry, but she impressed others as authentic.

This go-round, her speaking style and persona are well-timed for the political moment, said Republican pollster Frank Luntz. Her speech at the Democratic National Convention “was so good that it caused people to reevaluate her role and her capabilities,” he said.

Throughout her husband’s presidency, Michelle Obama has maintained the patina of a reluctant political spouse, focused squarely on raising her children successfully while advancing causes she cared about. Her public missteps came early and were few. All the while, she has honed her oratorical skills in smaller venues. For example, she had previously shared the story of “when they go low, we go high” during a commencement speech at Jackson State University, a historically black college in Mississippi.

Tucked into her remarks on the campaign trail and in quieter moments as she holds many of her final events as first lady, Obama has begun to reflect publicly on life after the White House and her legacy.

She had infrastructure installed around the White House kitchen garden that she planted, in the hope that it would become a permanent fixture. During her final “Let Girls Learn”event as first lady, she said that she would continue advocating for girls after leaving the White House.

Obama has also said that she is looking forward to the freedom and increased privacy of life outside the White House, but there are indications that she wants to continue to influence culture. She has already begun writing her memoir and has been involved in the planning of the Obama library; she told the crowd Thursday that she plans to remain engaged in the nation’s civic life for years to come.

The national spotlight does not usually follow first ladies after they leave the White House, said Katherine Jellison, a history professor at Ohio University who has studied first ladies, but there are exceptions. Eleanor Roosevelt, Jacqueline Kennedy and, of course, Clinton, remained dominant forces in public life.

“Since Michelle Obama has been such a megawatt first lady, she may be one of those exceptions. She is a celebrity,” Jellison said. “She can have a long post-White House period where she will probably continue some of her current projects, [and] she has political skills, although she keeps denying wanting that role for herself.”

For her part, Obama had this to say in Phoenix: “Hillary has comprehensive policies to help people. Her opponent has tweets. You decide.”

Abby Phillip in New York contributed to this report.