Linda Lingle's office also received dozens of angry calls, many of them saying they would not travel to the state.
Gay-rights activists began discussing retaliatory actions within hours of Lingle's decision, but as of Wednesday had made no decisions.
Still, the Internet was abuzz with expressions of anger, with Twitter users from California to New York urging people to avoid the Aloha State and at least two mainland bloggers asking readers if a boycott was justified.
Karen Ocamb, who writes about gay issues for Los Angeles-based blog LGBTPOV.com, wrote that a boycott is a "particular consideration for those in Southern California who pop over to Hawaii for a long weekend, believing it to be a warm, beautiful, welcoming state."
"How many might reconsider that trip now?" Ocamb wrote.
Robin Tyler, who heads a Los Angeles-area firm that organizes travel for women, said in an e-mail that she and her partner will not return to Hawaii next year as planned because of Lingle's veto.
"I don't think the southern states that practiced segregation expected a huge number of African-American tourists to come to see the scenery and enjoy the tourism aspect," said Tyler, who with her partner filed a legal challenge to California's same-sex marriage ban in 2004.
The governor's office also received dozens of angry calls, many of them saying they would not travel to the state. "Nine out of 10 seem to be from the mainland," Kaui Alapa, a receptionist there, told KITV. "They're angry and they want to boycott their vacation here and will spread the word to their friends not to come."
The idea of starting a boycott did not sit well with some leaders of Hawaii gay-rights groups, though they said more discussion of it is likely.
"We wouldn't want anybody to boycott Hawaii," said Tambry Young of Citizens for Equal Rights, one of several gay-rights groups that backed the civil unions bill.
Jo-Ann Adams, chairwoman of the Gay, Lesbian, Bisexual and Transgendered Caucus of the state Democratic Party, said a boycott would mostly hurt the hotel industry and its workers. She said some hotel chains and the labor union that represents tourism industry workers have been supportive of civil unions.
"We have to be very careful about what it is we say," Adams said.
Mike Golojuch Jr. agreed but said his anger over Lingle's veto led him to believe a boycott is justified.
"Money talks," said Golojuch, of Parents, Families and Friends of Lesbians and Gays-Oahu. "People need to fight back, and this is one way they can fight back, using their pocketbooks. So yeah, I would endorse a boycott."
For months, tourism representatives have been loath to discuss civil unions and their affect on Hawaii's No. 1 industry.
On Wednesday, in response to a question about boycott rumblings, Hawaii Tourism Authority President Mike McCartney said in a statement: "At this time, we are monitoring and assessing the situation to determine any appropriate response."
Former U.S. Rep. Neil Abercrombie, a Democratic gubernatorial candidates who support the civil unions bill, said those considering a boycott should let their emotions subside before making a decision.
"When the government in Hawaii is defending everybody's civil rights, that's going to have a positive effect on people coming," he said at a news conference.
In vetoing the bill Tuesday, Lingle said it was tantamount to same-sex marriage, which she opposes. She also said voters should decide whether marriage should be defined as between a man and a woman.