Taiwan's President Tsai Ing-wen nevertheless resigned as the chairwoman of the DPP following the election, and assumed responsibility for the significant defeat.
What next for China-Taiwan relations?
"Our efforts weren't enough and we let down all our supporters", the president said. However, Tsai insisted that Lai and Chen remain at their posts.
The election saw the opposition KMT, which is seen as more friendly towards Beijing, make gains, but much of the campaigning had focused on domestic issues such as living standards.
On Saturday evening it appeared the push for marriage equality in Taiwan had also suffered a set-back.
Seven million voters backed a definition of marriage as the union of one man and one woman.
Tseng Hsien-yin, leader of the Coalition for the Happiness of our Next Generation, a group that opposes gay marriage, said the decision reflected the will of the voters.
"Taiwan is a conservative society and not quite ready for the progressive label it's been given in some quarters", said Jonathan Sullivan, director of the China Policy Institute at Nottingham University.
In May 2017, Taiwan became the first country in Asia to legalise same-sex marriage but the government has been unable to implement its top court ruling in the face of conservative opposition.
Legislators in Taiwan offered differing opinions on whether President Tsai Ing-wen's administration would be required to pass laws reflecting the results of Saturday's referendum or would still be compelled to change the civil code to allow for same-sex marriage.
Ms Tsai said the DPP would reflect on the defeat, but she vowed to press on.
Beijing has refused to deal with Tsai's administration since she took office in 2016, accusing her of pushing for the island's formal independence.
More than 11,000 seats are up for grabs in municipalities, counties, townships and villages, with the southern city of Kaohsiung a key battleground for the ruling Democratic Progressive Party (DPP), which has held the city for two decades.
Beijing has been ratcheting up pressure on the island it claims as its own territory by poaching its diplomatic partners and barring its representatives from global gatherings, while staging threatening military exercises and limiting the numbers of Chinese tourists visiting Taiwan. Beijing has denied the allegations. As in previous elections it also tried to fuel fears about China.
The KMT - which lost the leadership and its majority in parliament two years ago as the public feared it had moved too close to Beijing - framed the election as a vote of no confidence in Tsai ahead of the vote, vowing to boost the economy and promote peaceful relations with China.
Analysts said the defeat ruled Tsai out as a candidate for the presidency in the 2020 election.
College student Kwan Chin-shun, 18, voting in Taipei, said she supported equal marriage rights.
Observers put the results down to anger over pension cuts and labor reforms, including slashing the number of public holidays, as well as concern that tensions with Beijing are damaging local business. It asks voters about whether Taiwan should change its name at worldwide sports events from Chinese Taipei to Taiwan, a move Beijing opposes.
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It would also be nice to see a more competitive side to the sport, which usually sees one side dominate the entire season. The team is looking at Charles Leclerc from Ferrari, Marcus Ericsson or Antonio Giovinazzi who is a reserve for Ferrari.
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This is because the each state has its own different set-up on all levels socially, financially and geographically. Each state has populations equivalent to nations with universal coverage hence size can never be a limiting issue.