The US transportation secretary, Pete Buttigieg, has delivered an emotional appeal for Republicans to support a law protecting same-sex marriage as it heads for the Senate.

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Democrats who control Congress aim to protect same-sex marriage amid uncertainty over which privacy based rights the conservative-dominated supreme court might target next, having overturned the right to abortion last month.

Appearing on CNN’s State of the Union, Buttigieg – the first openly gay cabinet secretary – was asked about dismissive remarks about the Respect for Marriage Act, which also protects interracial marriage, made by Marco Rubio, a Florida senator.

“If he’s got time to fight against Disney, I don’t know why he wouldn’t have time to help safeguard marriages like mine,” Buttigieg said.

That was a reference to Republican attacks on Disney over its opposition to legislation clamping down on teaching about LGBTQ+ issues in schools.

“This is really, really important to a lot of people,” Buttigieg said of the move to protect same-sex marriage, which the supreme court declared legal in 2015.

“It’s certainly important to me. I started my day, as I try to do on weekends, to get Chasten [his husband] a little bit of a break and do breakfast with both of our twins.