Although two-thirds of Taiwanese voters — some 7 million people — rejected the proposed reform in the November referendum, parliament passed a law legalising gay marriage to beat the constitutional court deadline of May 24.
The Coalition for the Happiness of Our Next Generation, one group seeking to overturn Taiwan's gay marriage law, said the public will "strike back" as it mobilised support to vote against Tsai in January elections, when she seeks a second term.
"If we can oust these legislators who supported same-sex marriage, there is a likelihood for change after 2020," said the group's president Tseng Hsien-ying.
"The only type of marriage people in Taiwan can accept is between a man and a woman. This [same-sex union] is destroying the institution of marriage and distorting our family values."
The lobby group Taiwan LGBT Family Rights Advocacy estimates about 300 same-sex families with children live on the self-ruled island, which China considers as its wayward province.
"It won't be an overnight change," said the group's spokeswoman Reese Li, adding that conservative groups are ramping up their smear campaign, including linking same-sex marriage to a potential rise in HIV cases.
"It will take time but once they see same-sex couples and families are no different than the others, they will accept it."