Police will get new powers under the bill
The bill easily cleared its Commons stage after just three days of debate thanks to the government's huge majority and the Conservatives' decision to abstain on the final vote.
But it faces an uncomfortable eight scheduled days of scrutiny by peers, which began on Tuesday afternoon.
'Ill-conceived'
The government has been accused of rushing through ill-conceived and "illiberal" legislation as a knee-jerk response to the terror attacks of 11 September.
Home Secretary David Blunkett told MPs that the measures were needed because Britain was still at risk from terrorist attacks.
Mr Blunkett wants the new measures, which include a new offence of incitement of religious hatred, on the statute books by the end of the year.
Serious opposition in the Lords could delay its passage into law.
'Counter-productive'
The Anti-Terrorism, Crime and Security Bill passed its final Commons stage on Monday, despite a rebellion by 21 Labour MPs and opposition from the Liberal Democrats.
Shadow home secretary Oliver Letwin warned the anti-hatred plans could prove counter-productive because they could prevent legitimate debate about religion.
Although action was much needed, he argued that the "ill-conceived proposals" failed to distinguish between race, which people could not alter, and religion.
New powers
Mr Letwin told BBC News he was worried the government was sneaking through new powers for the police to get confidential information under the guise of fighting terrorism.
The Tory spokesman hoped the Lords would insist on amendments.
Mr Blunkett has also come under pressure to ditch proposals to imprison foreign terrorist suspects without reference to the courts.
Significant concession
In his most significant concession offered so far, Mr Blunkett last week agreed to insert a "sunset clause", so the detention powers would lapse after five years unless backed again by MPs.
Liberal Democrat leader Charles Kennedy has said the plans would mean "suppressing our own individual rights" and hand a victory to the people behind the 11 September attacks.
He said his party agreed with "quite a lot" of the government's proposals, but more attention needed to be given to getting the "balance right".
'Not fit to be law'
Following Monday's vote, Lib Dem home affairs spokesman Simon Hughes said: "The terrorism bill as it finished in the Commons with large sections not debated was sadly not fit for the statute book and so we felt we had no choice but to vote against it.
"Any legislation approved by parliament must get the balance right between giving necessary powers to the state and upholding the individual's civil liberties.
"This bill has still got the balance badly wrong. We shall work with colleagues from all parts of the House of Lords to make significant amendments in the days ahead."