BETO O’Rourke may have lost his hotly contested Senate race in Texas against Republican Ted Cruz, but his celebrity supporters have already shrugged it off and are setting their sights on the White House for the risingDemocratic star.

“Beto lost? That’s OK. Now he can run for President,” actress Alyssa Milano wrote on her Twitter account shortly after the election was called for Mr Cruz.

Moments later she added: “#Beto2020.”

According to the New York Post, Olivia Wilde, whose mother, Leslie Cockburn, lost her congressional race in Virginia to Republican Denver Riggleman, said she was on board.

“Beto2020. Let’s do this,” the actress wrote.

Actress Busy Phillips, who has a new talk show in the US, suggested the Democratic ticket for 2020 should include O’Rourke and Andrew Gillum, the mayor of Tallahassee who lost his gubernatorial bid in Florida to Republican Ron DeSantis.

“Beto/Gillum 2020,” she posted.

Josh Gad, the voice of Olaf in Frozen, hailed Democratic gains in the House and looked into O’Rourke’s future.

“Looks like Dems will take the house! Do not let all of the other noise tonight deflate you. We finally have a check on the President. Tonight is a win for democracy. Oh and …#Beto2020,” he wrote.

Hours before Cruz officially defeated O’Rourke international news service Reuters informed its 20 million Twitter followers Tuesday afternoon that O’Rourke is a winner, regardless of whether or not he pulled off a shock victory over Cruz.

“Win or lose, Beto O’Rourke set to emerge victorious,” Reuters’ tweeted from its verified account, adding a link to the news gathering service’s Election Day coverage and a nearly two-minute, slickly produced video declaring O’Rourke victorious … one way or another.

O’Rourke, a three-term congressman and former El Paso city council member, was attempting to become the first Democrat to win statewide office in Texas since 1994.

O’Rourke, who amassed more than $US70million ($A96 million) in donations and gained nationwide exposure, lost a hard-fought battle against Cruz in Texas by a 50.9 to 48.3 per cent margin.

He was so fired up as he gave a concession speech to his fans in El Paso that he swore on live television.

“I want to thank this amazing campaign of people. All people all the time, all the time, in every single part of Texas, all of you, showing the country how you do this. I’m so f***ing proud of you guys,” he said.