In the biggest test of public opinion since Mr Blair became Prime Minister, called "Super Thursday", voters go to the polls in local-authority elections in most parts of England outside London.
There will be town-hall elections in Scotland and Wales and voting for the Edinburgh and Cardiff assemblies.
Mr Blair made a last-minute appeal for Scottish and Welsh voters to support Labour with both their assembly votes. They have one for a constituency representative under the first-past-the-post system and one for a party on a regional basis under the system of proportional representation.
The appeal reflected Labour fears that many voters will split their votes between different parties. This would enhance the prospects of the Scottish National Party and Plaid Cymru, which hope to deny Labour an overall majority in Edinburgh and Cardiff. "If you end up using a second vote for a different political party you will cancel out your first vote," Mr Blair said.
"It is vitally important people realise that, otherwise they can end up with a mish-mash of nationalist policies ... They can let them in by the back door, having decided rightly not to let them in by the front door."
Mr Blair was attacked by Paddy Ashdown, Liberal Democrat leader, who accused him of insulting the intelligence of the Scottish and Welsh people and who said they would not be fooled. "The Scots were the people who taught us tactical voting," said Mr Ashdown.
At separate press conferences Mr Blair and Mr Ashdown refused to discuss the prospect of a Lib-Lab coalition in the Scottish Parliament if Labour failed to win outright, as opinion polls suggest.
Privately, however, senior figures in both parties believe they would quickly reach agreement on a coalition.
More than 13,000 town-hall seats are being contested in 362 local authorities. Labour is worried that "a culture of contentment" with the Government will make it hard to persuade people to vote and that the turnout will be lower than the 29 per cent seen in last year's local polls.
Normally, governments suffer mid-term losses in local elections but this year the man with most to lose is William Hague, who is fighting for his job as Tory leader after recent turmoil in the party.
The Tories are bound to make big gains, since they recorded their worst election performance when the same seats were last contested in 1995. But Mr Hague may face moves to oust him unless his party gains more than 1,000 seats and improves on the 31 per cent share of the vote it won at the 1997 general election.
Colin Rallings and Michael Thrasher of Plymouth University, who study local elections, predict in this week's Local Government Chronicle that the Tories will gain 1,400 seats and win control of 30 authorities, with Labour losing 1,300 seats and control of 100 councils.