Both Labour and Liberal Democrat peers have now tabled motions to "kill" the welfare reforms.
They have been warned this move poses the risk of causing a constitutional crisis.
The Bishop of Portsmouth, Rt Revd Christopher Foster, tabled a "motion of regret" on Friday.
It says that the Government has "failed to take account of the short-term impact" that the cuts will have.
It is thought that this motion will be supported by a number of cross-bench peers.
Speaking to The Daily Telegraph, Lord Williams of Elvel, Labour, suggested that blocking these cuts would be "unwise".
He commented that it would present a "serious challenge" to the authority of the House of Commons.
However a cross-bencher as well as Labour and the Liberal Democrat party are all against the changes.
The potential Church of England bishops' motion means there are now reports that concessions may be made.
Threats to throw out the £4.4 billion cuts sparked warnings from David Cameron that peers should obey the convention that the House of Lords does not block financial policies approved by MPs.
The Conservatives say any blocking of the changes would be "unconstitutional" and would give the House of Lords new powers.
Lord Butler, a former Cabinet secretary and cross-bench peer, has warned that the House of Lords was "getting too big for its non-elected boots."
Prime Minister, David Cameron, has suggested he is prepared to flood the Lords with Conservatives if tax credit changes are blocked.
