Asked about the threshold, Burnham said: “I think social care in England is as unfair as American healthcare. The vulnerable pay with everything and it can completely leave them with nothing.
“That floor has been in place for a long, long time and common sense says it cannot be fair.”
Burnham said in “an ideal world” he would not want anyone to have to sell their home to pay for care, describing it as a “really awful process”.
He added proposals he previously put forward were intended to stop that, saying: “If everybody on the NHS principle contributed a little, it would mean everybody could protect the majority of what they’d worked for.”
Burnham said he did not know if people support that approach, adding this was for something for the consultation to consider.
On the cross-party talks, Burnham said there has been 22 failed attempts to make progress in almost 30 years.
The PM said: “We’re going to have to find common ground here if this is to be a lasting solution.”
Lib Dem leader Sir Ed said the first “constructive” discussion had left him feeling “hopeful” and more meetings will be required to find consensus.
He said: “Everyone will have to accept things we might not like in order to work together – but I think that’s what the public want and expect us to do.”
Sir Ed, who has a disabled son who needs round-the-clock care, said the system “just isn’t working” and any solution must have family carers “at its heart”.
Reform Treasury spokesman Robert Jenrick said: “Make no mistake, today Andy Burnham fired the starting gun on his scheme to raid the little money that hundreds of thousands of regular people have struggled to save over their lifetimes.
“That’s why he can’t rule out the new universal death tax.”
Green Party social care spokesperson Ellie Chowns said: “If Andy Burnham is serious about doing things differently and tackling the crisis in care, he must work collaboratively with the Greens and other parties to do so.”