To those who do not want to see the US president run for re-election, Joe Biden has a message: “Watch me.”

A self-assured Biden, riding high from Democrats’ history-defying showing in this year’s midterm elections, said at a post-election press conference that he intends to seek another term, but that it was ultimately a “family decision”.

“I think everybody wants me to run, but we’re going to have discussions about it,” Biden told reporters, indicating that he would sit down with his family over the holidays and announce his decision “early next year”.

A full accounting of the election results will take several more days, or possibly weeks, to know as key states continue counting and a Senate race in Georgia heads to a runoff that could determine control of the chamber.

Though Republicans hold the edge in the district-by-district battle for the House, Biden and his party managed to avoid the “giant red wave” that many Democrats had braced for in a political environment shaped by widespread economic discontent and the president’s low approval ratings. Control of the Senate also remains within reach for Democrats.

Despite the unexpectedly strong showing Biden, approaching his 80th birthday this month, could still face strong headwinds in 2024. Two-thirds of midterm voters said they would not like to see Biden seek re-election in 2024, according to exit polling conducted by Edison Research. That includes more than 40% of Democrats and 90% of Republicans, the poll showed.

But the surprising, mixed results on Tuesday may serve to bolster Biden’s case for seeking re-election and perhaps even quell concerns among those in his party who hope the party elects another standard-bearer in 2024.

“Our intention is to run again,” Biden said. “That’s been our intention regardless of what the outcome of this election was.

In the months before the election, vulnerable Democrats were peppered with questions about whether they would support Biden in 2024. And Democratic leaders have mostly delicately sidestepped questions about whether he should run again.

For now, Democrats’ successes have shifted the attention to Donald Trump, who hoped a wave of Republican victories would propel the launch of his third presidential bid, expected as soon as next week.

But many of Trump’s hand-picked candidates lost on Tuesday night, among them Mehmet Oz, the celebrity doctor, who lost a marquee Senate race in Pennsylvania to John Fetterman. The underwhelming results have raised questions about the former president’s political strength, with some openly warning that he is a drag on the party.

Meanwhile, Trump’s chief Republican rival, the Florida governor, Ron DeSantis, cruised to re-election on Tuesday. Following DeSantis’s strong performance on Tuesday, in which he expanded his support among Hispanic voters and turned the increasingly Republican state even redder, many conservatives are already pushing him as a promising alternative to Trump. The conservative New York Post anointed DeSantis as “DeFuture”.

Biden welcomed the Republican competition. “It would be fun to watch them take each other on,” he said.

Even before the president makes a decision, his team has started to lay the groundwork for a potential campaign.

“We are engaged in some planning for the simple reason that if we weren’t engaged in planning in November of this year, we should be in the political malpractice Hall of Fame,” said Anita Dunn, senior White House adviser, during an Axios event last week.

Biden’s approval rating stands at 43% among registered voters, according to a Washington Post-ABC poll released ahead of election day. But he remains popular among Democrats, with eight in 10 giving him positive ratings compared with nine in 10 Republicans who disapprove of his job performance. Slightly fewer than four in 10 independent voters say they approve of his performance.

There appears to be little appetite among elected Democrats to challenge Biden in a primary. The Vermont senator Bernie Sanders, a leading progressive, has ruled out a run against Biden.

Should Biden choose not to run, it’s unclear who would step forward to seek the nomination.

As vice-president, Kamala Harris is seen as an heir apparent, and would probably emerge as the frontrunner. Harris, who campaigned across the country for Democrats this cycle, was credited with spotlighting the issue of abortion and reproductive rights, which proved decisive in key races. But she, like Biden, also suffers from low approval ratings.

Other Democrats have attracted 2024 speculation. The Minnesota senator Amy Klobuchar and the transportation secretary, Pete Buttigieg, both of whom ran in 2020, traveled to several states this cycle to campaign for Democrats.

California’s governor, Gavin Newsom, who easily won re-election on Tuesday a year after defeating a recall attempt, has sought to build a national profile by publicly challenging DeSantis. And Michigan’s governor, Gretchen Whitmer, who stormed to re-election in a battleground state, is seen as a rising star.

David Shor, a top Democratic data analyst, said the midterm results underscored the power of incumbency, as many of the party’s endangered members held on to their seats despite a challenging political environment. Rallying behind an incumbent also avoids a messy primary, he said.

“There’s definitely a case that it would make sense to avoid a bruising, trillion-dollar primary where all of the smartest minds in the Democratic party devote themselves to driving the favorables down of all of our favorite candidates,” Shor said in an interview on the Guardian’s Politics Weekly America.

But the bigger variable, Shor argued, could be the economy.

“The traditional pattern of American politics was that there was this really strong relationship between economic conditions and presidential approval. That was true for Clinton, it was true for Bush but it stopped being true for Barack Obama and for Donald Trump. But it’s come back for Joe Biden,” he said. “And so I think ultimately, the question of 2024 is really just what the economy ends up being.”