The hospital was criticised by the Healthcare Commission last March
Relatives angered by failings in care at a hospital are meeting David Cameron to discuss opening a public inquiry.
A damning Healthcare Commission report last year said about 400 more people died at Stafford Hospital between 2005 and 2008 than would be expected.
The Conservatives and Lib Dems have promised to hold an inquiry if they win the general election. Labour said it would do more harm than good.
An independent inquiry is currently being held in private.
Campaigners from Cure the NHS are at Westminster on Tuesday.
The group - made up of relatives who died at the hospital and those who feel they were victims of poor care there - want to know how the hospital was allowed to gain Foundation status when the death rates were so high.
The campaigners have been calling for a public inquiry for some time following the publication of the Healthcare Commission's report last March.
The hospital was criticised for its "appalling" emergency care during 2005 and 2008 that led to patients "dying needlessly".
Mid Staffordshire NHS Foundation Trust was given a "weak" rating last October by new regulator Care Quality Commission (CQC).
The trust apologised to families on the first day of the current inquiry.
It is thought the findings are due to be released later this week.
Shadow health minister Stephen O'Brien, has told the BBC that the Conservatives would hold a statutory-based public inquiry "within weeks and months" of the election if the party forms a government.
The inquiry would mean witnesses would be compelled to give evidence.
'Hole in the head'
Mr O'Brien, MP for Eddisbury, said: "It's absolutely vital we learn all the lessons that must be learned from the appalling events that took place at Mid Staffordshire Trust and Stafford Hospital.
"We have to see what happens after the general election.
"If we do form a government, we have made a commitment to (campaigner) Julie Bailey and Cure the NHS campaign.
"I put this to them when I met met them and I have confirmed that we would establish a full public inquiry as soon possible after we are elected."
But health minister, Mike O'Brien, said it would not help.
"I think the price of that would be to cause some problems for the hospital," he said.
He added that he thought the hospital needed an 18-month public inquiry "like a hole in the head".