Alistair Darling's role as chancellor may soon be "untenable" following a series of "disasters", Liberal Democrat acting leader Vince Cable has said.
Mr Darling blamed the missing discs on a junior offficial
The only reason Mr Cable said he was not calling for Mr Darling's head was that the problems facing him "relate to decisions made by Gordon Brown".
Mr Cable added his voice to Tory calls for a fresh statement from Mr Darling on the lost benefit data scandal.
Ministers have said the government is handling that and other problems well.
Justice Secretary Jack Straw said Mr Brown was a "very good crisis manager" and the HM Revenue and Customs HMRC missing data "debacle" had been managed "as well as any government could have anticipated".
He also defended Mr Darling, telling BBC1's Sunday AM the chancellor had been "completely upfront" about the situation and was a "man of honesty".
Mr Darling told MPs on Tuesday a junior HM Revenue and Customs employee was to blame for two computer discs containing 25m claimants' details going missing.
But shadow home secretary David Davis said documents suggested senior officials were aware of what happened.
Mr Davis called on Mr Darling to explain to MPs at what level within the HMRC management bulk despatch of personal data was sanctioned.
And he challenged Mr Darling's claim that the mailing was the responsibility of a single junior member of staff acting in breach of HMRC procedures.
Mr Davis told Sunday AM: "We are demanding that Alistair Darling comes back to the House because we don't know if we have been told the truth, but we certainly haven't been told the whole truth about this episode."
MPs were no longer sure "whether this was a civil service failure, let alone a civil service failure by a lone member of staff" rather than the result of faults in the system imposed by ministers, said Mr Davis.
Mr Brown was responsible not only for merging the Inland Revenue and HM Customs and Excise, but also for transferring responsibility for dispensing child benefit to the agency, making its work significantly more complex, he said.
And he added: "I think accusing a junior member of staff of being responsible for this whole problem is at best ignominious and at worst dishonourable."
Mr Davis said he believed the loss of HMRC data had also brought home to the public the dangers of introducing ID cards.
Mr Cable also called for a Commons statement from Mr Darling.
He told BBC1's The Politics Show: "There has been a whole succession of disasters this week and it may well be that (Mr Darling's) position is untenable eventually."
Asked if that point was getting close, he replied: "It may well be."
But he added: "I am not arguing for Alistair Darling to go, for one major reason. Almost all of these problems - and we have had a succession of them: Northern Rock; the lost files; the Qinetiq sale; the criticism of defence spending - most of these relate to decisions made by Gordon Brown when he was Chancellor of the Exchequer.
"So it is really his decisions which are coming under scrutiny."
Mr Cable said he was concerned that "bad political decisions" ultimately led to HMRC's loss of confidential data.
"We do know that there were massive economies of staff which led to the department being under-supervised and low morale," he said.
Mr Cable said he was "alarmed" by an email released by the National Audit Office, which appeared to suggest that security measures were rejected by HMRC on cost grounds.
"There really has been a culture of penny-wise, pound-foolish behaviour in that department," he said.
LOST CDS - SEQUENCE OF EVENTS
18 October - Junior official from HMRC in Washington, Tyne and Wear, sends two CDs containing password-protected records to audit office in London through courier TNT, neither recorded nor registered
24 October - When package fails to arrive, second one is sent by registered post and arrives safely
3 November - Senior managers are told first package has been lost
10 November - Prime minister and other ministers are informed
12 November - HMRC tell ministers CDs will probably be found
14 November - When HMRC searches fail, Metropolitan Police are called in
15 November- Richard Thomas, Information Commissioner, says remedial action must be taken before public is informed
20 November - HMRC Chairman Paul Gray resigns; Chancellor Alistair Darling makes announcement to House of Commons
21 November - Prime Minister Gordon Brown apologises and orders security checks