Control of the US Congress hung in the balance on Wednesday after Democrats put up an unexpectedly strong fight in the midterm elections, while Republicans insisted they were on course to take back at least the House of Representatives.

Republicans notched up a string of convincing victories, particularly in Florida, where governor Ron DeSantis cruised to re-election by a 20-point margin. But while the House appeared to be within the grasp of Republicans, control of the Senate remained too close to call, as Democrats appeared to stave off the worst-case scenario that many polls had predicted.

“It’s not a wave for sure,” said Lindsey Graham, the Republican senator from South Carolina, referring to the “red wave” that many pollsters had predicted heading into Tuesday’s election. However, Graham said his party was on course for a “very good night” and predicted it would win a majority in House.

Republicans need only a net gain of five seats to win a House majority and still have the edge in the lower chamber, as votes were still being counted on Wednesday. But they may take control with a smaller margin than they hoped.

In a delayed victory speech delivered at 2am local time, Kevin McCarthy, Republican leader in the House of Representatives, said: “When you wake up tomorrow we will be in the majority and Nancy Pelosi will be in the minority.”

Pelosi, the Democratic Speaker of the House, issued a statement saying her party’s members were “strongly outperforming expectations” and “every vote must be counted as cast”.

Frank Luntz, the Republican pollster, said the party may have placed too much emphasis on opinion polls that suggested they would perform strongly. “This is not a tsunami . . . I think that Republicans got ahead of themselves,” he told the Financial Times.

The best early result for Republicans was in Florida, where DeSantis, seen as a probable contender for his party’s presidential nomination in 2024, was quickly projected to win re-election, along with senator Marco Rubio.

“I look forward to the road ahead,” DeSantis said after his victory. “We have accomplished more than anybody thought possible four years ago. But we have got so much more to do and I have only begun to fight.”

Luntz called DeSantis “the real winner” of the midterms. “He has turned a successful governorship into a nationwide movement. I think he is going to give [Donald] Trump a run for his money.”

However, despite the strong showing in Florida — which had until recently been seen as a swing state — the results were more mixed in other battleground contests. Pivotal Senate races in Georgia, Arizona and Nevada remained exceedingly tight, with highly uncertain outcomes.

In the key swing state of Pennsylvania, Democrat John Fetterman delivered a major victory for Democrats by winning the Senate seat vacated by the Republican Pat Toomey. Fetterman’s campaign had been hampered by his recent stroke.

Fetterman positioned himself as a working-class progressive, almost always appearing in a hoodie and shorts. “This race is for the future of every community all across Pennsylvania,” he told supporters. “For every small town or person that ever felt left behind.” The White House said Biden had sent Fetterman his congratulations by text message.

Democrats held on to several bellwether House districts on the east coast where their candidates were seen as vulnerable, with victories for Abigail Spanberger in Virginia and Seth Magaziner in Rhode Island.

Meanwhile, New York governor Kathy Hochul was re-elected after holding off Republican challenger Lee Zeldin. The result will bring Democrats some relief after polls showed Zeldin closing a yawning gap in recent weeks with a relentless focus on crime.

The White House, which had been bracing itself for heavy losses in the House, in particular, said Biden had started to call Democrats, including Spanberger and Senate majority leader Chuck Schumer, to congratulate them on winning their races.

Even a small majority in the House for the Republicans threatens to stymie the next two years of Biden’s presidency. Republican leaders have suggested that they will use the debt ceiling as leverage to push through their own policy priorities, such as cuts to federal spending.

They have also indicated they will disband Democrat-led investigations, including the special committee probing Trump’s role in the January 6 2021 attack on the US Capitol, and launch their own inquests into everything from the origins of the Covid-19 outbreak to the business dealings of Hunter Biden, the president’s son.

Republicans notched a number of high-profile wins outside of Florida too, with Texas governor Greg Abbott winning re-election and JD Vance, the former venture capitalist and author backed by Trump, winning his Senate race in Ohio.