Two major opinion polls on Tuesday put the "No" side lead at 11 percentage points with just days to go before the vote.
Another poll showed the "No" side's lead widening slightly just when euro supporters need to persuade the many waverers to give up the krona.
But as campaigning hit fever pitch, Prime Minister Goran Persson insisted victory for the "Yes" side was still possible.
Euro supporters pin their hopes of Sweden becoming the 13th member of the single currency on politicians and business leaders drumming up late support.
But opposition to the euro is being shored up by fears it might put at risk Sweden's generous welfare system and political control over its prosperous economy.
Euro sceptics have led the polls since April, although the gap has narrowed slightly since then.
Persson hopes for a repeat of Sweden's 1994 referendum on EU membership, when the undecided turned pro-EU late in the game.
"This will be an extremely close race. I have said that all the time. And many, many voters will decide on the last day of the week," said Persson as he cast an early postal vote.
But Ulla Hoffman, head of the anti-euro Left Party, said: "People trusted the politicians in 1994 but they won't trust them this time."
Many Swedes express concern about delegating policy to the European Central Bank when their economy has been performing better than the euro zone.
"The economic fundamentals show that Sweden is doing quite well out of EMU," said a Deutsche Bank report.
In the second quarter of 2003 Sweden's economy grew 1.3% year-on-year versus euro zone growth of 0.2%.
Euro zone recession
Meanwhile, Europe's beleaguered economy is close to recession, data confirmed on Tuesday.
But officials forecast the 12-member euro zone will pull back from the brink over the next few months.
Persson (L) hopes undecided
voters will swing the result
The European Commission, battling to persuade key euro zone states to respect strict budget rules, described the new figures as disappointing.
According to the European Union, gross domestic product in the zone sharing Europe's single currency contracted by 0.1% in the second quarter after stagnating in the first.
Interest rates cuts
The downward revision has dashed any hopes of a strong recovery and highlighted the need for further interest rate cuts, economists said.
"Our view is that the ECB (European Central Bank) will need to deliver more in the way of rate cuts by the spring," said Lehman Brothers economist Michael Hume.
"It is clearly not in the mood to cut rates at the moment, but that can't last."
The figures put the bloc dangerously close to a recession, defined as two consecutive quarters of economic contraction.
But the commission, the EU's executive arm, forecast the economy would pick up in the third and fourth quarters, predicting GDP growth of 0-0.4% and 0.2-0.6% respectively.
"The acceleration in growth predicted for the fourth quarter stems from the recent improvement in domestic retail confidence, as well as external factors," said the EU executive in a statement.
Hume commented on the downward revision by saying: "The numbers were pretty dreadful but didn't contain much in the way of surprises.
"The domestic side was a bit weaker, so that was a bit disappointing as it suggests that the recovery - and I do think we are seeing a recovery - is still too much dependent on the recovery in the US and to some extent in the Far East."