David Cameron and Nick Clegg are expected to enter opposing division lobbies as the Liberal Democrats seek to thwart Conservative plans to redraw parliamentary boundaries before the next general election.
The Prime Minister wants to overturn a Lords defeat that means the boundary review - which could hand the Tories up to 20 extra seats - will not be implemented until after the 2015 election.
But with the Tories short of a majority in the Commons, Downing Street acknowledged that "the arithmetic looks pretty difficult".
Mr Clegg, the Lib Dem Deputy Prime Minister, announced last summer that his party would try to delay the review after the Tories forced the abandonment of plans to reform the House of Lords.
Earlier this month Lib Dem peers combined with Labour to back an amendment delaying plans for a boundary review and to cut the number of MPs until after the next general election.
Six of the seven Lib Dem frontbenchers in the upper chamber joined the revolt - the first time in this Parliament that ministers in either House have voted against the Government.
The Prime Minister's spokesman said yesterday that "the application of collective responsibility has been set aside" for the Electoral Registration and Administration Bill.
Asked if Mr Cameron was confident of overturning Lords amendments, the spokesman said: "From the Prime Minister's perspective, the arithmetic looks pretty difficult."
He added: "The Prime Minister's view is that it is very important that this issue comes before the House of Commons. The Prime Minister's view is that he is strongly in favour of smaller, cheaper and fairer politics but it is important that MPs can consider the issue."
The spokesman indicated that no talks were under way with smaller parties in the hope of securing enough votes to force the Bill through.
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