Peers are expected to give the Safety of Rwanda Bill a rocky ride when it returns for debate on Monday.
The upper chamber is packed with lawyers and the Conservatives do not have a majority.
It means the scrutiny role is likely to take months, with Easter expected to be the earliest it finishes its Lords stages.
Peers are expected to make many amendments to the bill, which will then be sent back to the Commons for MPs to consider.
The government is unlikely to accept many, if any, of the changes, so the legislation will ping pong back and forth between the two Houses as they respond to one to each proposal.
Parliament must also sign off the new treaty with Kigali drawn up to address concerns raised by the Supreme Court. Peers want extra safeguards to stop anyone being deported from being sent on to another country once they reach Rwanda.
Although the Bill stops most grounds for individuals to appeal it does not prevent claimants from going to the European Court of Human Rights.
Prime Minister Rishi Sunak insists he is prepared to ignore “pyjama” injunctions that stop deportations.
