Nearly four decades ago, a group of lawyers, intellectuals and activists assembled in a hotel ballroom in Taipei to found an illegal political party dedicated to ending authoritarian rule in Taiwan.

No longer a scrappy upstart, the Democratic Progressive Party, born in that ballroom, is now seeking an unprecedented third consecutive term. It needs to persuade voters that after eight years in power, the party can renew itself while also protecting Taiwan from mounting pressures imposed by Beijing, which claims the island as its territory.

Led by Vice President Lai Ching-te, the presidential candidate, the D.P.P. faces a stiff challenge in an election on Saturday from its chief rival, the Nationalist Party, which favors expanded ties with China. Polls have indicated that the Nationalists, led by Hou Yu-ih, a former policeman and the mayor of New Taipei City, may have a fighting chance of returning to power for the first time since 2016, an outcome that could reshape the region’s geopolitical landscape. Election results are expected by Saturday night.

For Su Chiao-hui, a lawmaker with the Democratic Progressive Party, the stakes of the vote are especially personal. Her father, Su Tseng-chang, helped found the party when Taiwan was under martial law and later served as a premier in both the party’s two phases in power, including under the current president, Tsai Ing-wen.

“I’m a child of the D.P.P.,” Ms. Su, a lawyer, said in an interview, recalling seeing her father take part in pro-democracy protests. “Those are the memories in my bones, my daily life, so I didn’t need to march on the streets to know that politics can have a big impact.”

The challenge for Ms. Su and her generation of D.P.P. politicians is to persuade voters that the party can deliver the right mix of change and continuity: Change in response to concerns about slowing growth, rising housing prices and other livelihood issues.

Yet also continuity: assurance that a new D.P.P. administration would not rock Ms. Tsai’s measured approach to China, and is best qualified to keep Taiwan safe.

Over the past decade, the question of Taiwan’s future has become a major flashpoint in tensions between China and the United States, shaping debates in Washington and globally.

The D.P.P., which has long rejected Beijing’s demands for unification, has been at the heart of transforming the island into a geopolitical bastion against Chinese power. President Tsai has worked to steer Taiwan out of China’s powerful orbit, enhancing ties with Washington and raising the island’s global profile.

But after two terms, Ms. Tsai must step down this year. Polls indicate that sizable numbers of Taiwanese voters would like fresh leadership. A growing number worry about rising risks of conflict with China, which has denounced the D.P.P. as a party of separatists, and has cast Taiwan’s election as a “choice between war and peace.”

Mr. Lai has vowed to continue Ms. Tsai’s steady course. Yet even if Mr. Lai wins, his party may well lose its majority in Taiwan’s legislature, giving the opposition greater influence.

Ms. Su, 47, is working to persuade voters to give the party four more years of majority rule to allow Mr. Lai to advance his agenda if he wins. She courts voters at night markets and crossroads, accompanied by “Otter Mama,” her bespectacled, pink-clad campaign mascot, who features on a children’s show promoting the local Taiwanese language.

Her father, Mr. Su, 76, an energetic speaker at election rallies across Taiwan, sees the party’s legacy at stake — as well as his own.

“We have worked so hard to finally get out of authoritarianism and finally achieve democracy, freedom and openness,” Mr. Su said. “If we cannot hold onto these achievements and instead turn back, then I’m afraid that the lifelong struggles and striving of my contemporaries will be in vain.”

As a young lawyer, Mr. Su, the son of a minor official whose family raised pigs to make extra money, joined a grass-roots movement of pro-democracy lawyers, academics and activists. They were seeking to end the military reign of the Nationalists, who had ruled Taiwan since fleeing there in 1949 after the Communists took control of mainland China.

That resistance led to the meeting in 1986, in the unlikely setting of the Grand Hotel Taipei overlooking Taipei. The ornate hotel was established as a symbol of Chiang Kai-shek’s authoritarian rule — he and his wife had their own set of rooms inside — and yet it became the birthplace for the party that hastened Taiwan’s transition to democracy.

On a recent morning, Mr. Su showed reporters from The New York Times around a ballroom of the hotel, recalling the day that the party came into being there. Activists had booked the room on the flimsy pretext that they were a dentists’ association. Hours into their meeting, they approved a decision to form the party, catching the security police by surprise.

Though the Nationalist government had already begun to fitfully relax political restrictions, it still outlawed opposition parties. Even so, it chose not to break up the new party, fearing a backlash at home and abroad. The following year, it ended four decades of martial law.

As the Nationalists liberalized and Taiwan moved to democracy, D.P.P. politicians sought to galvanize support by calling for Taiwan’s formal independence. In 1991, the party declared in its platform that its goal was a “Republic of Taiwan as a sovereign, independent, and autonomous nation.” But quickly, questions of what independence meant and how it should be realized caused tensions for the party.

That 1991 platform worried both Washington and many of the island’s voters, who then and now, have shunned any move toward formal independence, fearing a wrathful reaction from Beijing.

The party, under politicians like Mr. Su, adjusted its line, arguing that Taiwan was already, in fact, independent, because its people had won their democratic self-determination.

“China has never ruled us for one day, and no part of us belongs to China,” Mr. Su said, “so we make the point that actually we are already independent, and there’s no need for a further declaration of independence.”

When the Nationalists tried to cast the party as a dangerous mob, Mr. Su and other D.P.P. politicians turned to friendly, humorous imagery to try to reassure voters it wasn’t a threat. In one campaign, Mr. Su was accompanied by his mascot, a dancing bright orange lightbulb, its shape mimicking Mr. Su’s bald head.

The party first came to power in 2000, when its candidate Chen Shui-bian won an upset victory for the presidency. But Mr. Chen subsequently drew criticism from the United States for his combative pro-independence moves, and he was later jailed for corruption. In 2008, the Nationalist candidate, Ma Ying-jeou, swept to power.

The D.P.P. turned to Ms. Tsai, a politician, who offered a professorial demeanor and a cautious stance toward Beijing. Ms. Tsai reinvigorated the party, and in 2016 she won the presidency along with a majority in the legislature.

Mr. Su served as the premier under Ms. Tsai from 2019 to 2023, and he counts among their achievements shielding Taiwan from the worst of the Covid pandemic and legalizing same-sex marriage, the first Asian government to do so.

Mr. Su is still widely recognized by many voters, and his speeches — delivered in a booming, gravelly voice — often win big applause at rallies, where he shouts his Taiwanese-language slogan, “Tshiong! Tshiong! Tshiong!” (“Rush, rush, rush!”)

Mr. Su also acknowledges that the Democratic Progressive Party “does not have a perfect score” among voters. Higher prices for housing and other economic strains have fueled discontent, particularly among the youth. But, he argues, the Nationalists’ record in power has been worse.

The D.P.P. candidate, Mr. Lai, has led the polls in recent weeks, but by a narrow margin. Mr. Hou, the Nationalists’ candidate, has trailed by a few percentage points in many polls. And an insurgent candidate — Ko Wen-je, the leader of the Taiwan People’s Party — has eroded support for both parties, especially among younger voters.

The Nationalists have argued that Mr. Lai is less steady than Ms. Tsai, and they cite Mr. Lai’s earlier remarks that he was a “pragmatic worker for Taiwan’s independence.”

But in the D.P.P.’s strongholds in southern Taiwan, many of the party’s politicians said there was no groundswell for seeking formal independence. They expect Mr. Lai to stick to the status quo, and support that strategy. Many younger party activists are more passionate about social issues than about talk of independence.

“Many Taiwanese people nowadays may not say clearly or strongly ‘I support Taiwan independence or unification,’ but everyone has an understanding that we’re not the same country as China,” said Chang Che-wei, 28, a political aide to Ms. Su. “Of course, I hope to keep the peace, but I think that it would be better to maintain a beautiful distance.”