Mr Blunkett wants the bill to become law by Christmas
Peers have approved plans to force the home secretary to renew parts of the legislation every one, two or five years.
However, the government avoided defeat over plans to introduce European Union legislation to combat terrorism after Home Secretary David Blunkett agreed to limit its scope.
The bill is due to receive its third reading in the Lords on Tuesday before returning to the Commons later in the week.
Continuing opposition from peers could seriously hamper Mr Blunkett's attempts to get it on to the statute books by Christmas.
'Consensus possible'
Shadow home secretary Oliver Letwin told BBC Radio 4's Today programme on Tuesday his party did not want to hold up the legislation.
"I am fully convinced that we can have this Bill through well in time for the Christmas break," said Mr Letwin.
"What we're looking for Mr Blunkett to do now is to be statesmanlike, calm down, come to the House of Commons, sit down with the other parties and agree about these things."
Mr Blunkett continues to insist the new laws are essential because the UK is still at risk from terror.
Last week he saw his plans mauled by the House of Lords, when peers defeated the government seven times.
Since then the home secretary has made a series of compromises in an effort to win over critics, including a commitment to review the entire bill within two years.
He has offered a wholesale assessment of the bill because of its complexity and the speed of its passage through Parliament, saying such a move was the "act of a listening government".
Matters of religious hatred will be referred to the attorney general, he said in another attempt to appease his critics.
Lord Goldsmith, the current attorney general, says he would not consent to prosecution where conduct "consists of the legitimate expression of religious belief".
He told peers: "We cannot and should not forget that ordinary people on our streets face hatred and harassment because others hold misguided prejudices about their beliefs."
His words were not enough to convince opposition peers, who argue the clauses should not be part of the emergency legislation.
Warning letter
Earlier, the home secretary sparked fury among his opponents over the letter he sent to Tory leader Iain Duncan Smith urging him to rein in his peers.
In the letter he warned amendments to the bill introduced by the Lords would have "dangerous consequences".
In response, Liberal Democrat leader Charles Kennedy said Mr Blunkett was behaving in a "dangerously illiberal" way.
Lib Dems and Conservatives have vowed to continue their opposition in Parliament, although they also pledge to work to reach a consensus.
The Lords will continue to debate the bill until Tuesday when it will return to the Commons for its third reading.
'No bullying'
On Monday, Downing Street continued to stress the importance of the legislation.
The prime minister's official spokesman said the government was determined the bill would have teeth.
"We are not prepared to be filleted, gutted or emasculated," he said.
The spokesman argued it was not the mark of a "bullying" government to listen as it had done by making the various concessions.