Vote 2011: Clegg fights back with NHS pledge
Nick Clegg has promised "a louder Lib Dem voice" in government and says he will show the party is "a moderating influence on the Conservatives".
The Lib Dem leader said he expected significant changes to the planned NHS revamp and would block the legislation unless he was happy with it.
But he told the BBC there would be no redrawing of the coalition agreement.
The Lib Dems suffered huge losses in Scottish and English elections and were defeated in the AV referendum.
At present, the controversial NHS reform bill - which would give GPs control of much of the NHS budget - is currently on a "pause" in its progression through Parliament while the government listens to concerns.
BBC political correspondent Norman Smith said there would be some disquiet among MPs that Mr Clegg had signed the NHS White Paper, but was now talking so stridently about wanting changes to it.
Thursday's referendum was a key concession secured by the Liberal Democrats as the price of forming a coalition government with the Conservatives.
But the rejection of the proposal by 13,013,123 votes to 6,152,607 potentially marks a new phase in the relationship between the two parties.
The Lib Dems also lost around 700 councillors in the English local elections - more than a third of the seats they were defending - and 12 of its 17 MSPs at Holyrood, where the SNP scored an historic victory.
Critics have suggested the party could be wiped out at the next general election unless they do more to re-establish their party identity within the coalition.
Deputy Prime Minister Mr Clegg told the BBC's Andrew Marr programme that Lib Dem ministers were committed to the plans set out in the coalition agreement, but they needed to work harder to get their voice heard by the public.
"Where we achieve Liberal Democrat policies in government, we've got to tell people about it," he said.
"We've got to show people where we are a moderating voice on the Conservatives. We need to stand up for our values and say that loud and clear."
Mr Clegg said the pause in the NHS changes was "absolutely not just for the sake of it" and getting the bill right was "now my number one priority".
"This is a not a cosmetic exercise," he said. "There will be substantial and significant changes to the legislation. As far as government legislation is concerned, no bill is better than a bad one and I want to get that right.
"A lot of people have said to me - and I basically think they're right - 'You're going too fast, you're trying to meet artificial deadlines, you're forcing GPs to take on commissioning roles when they don't want to or aren't able to.'"
Mr Clegg said he wanted guarantees that there would not be "back-door privatisation" of the NHS, and the Lib Dems would not allow the bill to be passed "unless I personally am satisfied that what these changes do is an evolutionary change, not a disruptive revolution".
Lib Dem deputy leader Simon Hughes told the BBC's Politics Show there should be "no privatisation at all" of the NHS, but Defence Secretary Liam Fox said that was "as wrong as [saying] all provision should be in the private sector."
MPs will discuss the NHS in the Commons on Monday, and ahead of that debate, shadow health secretary John Healey said he was glad the Lib Dems were "starting to make the arguments Labour has been making since the early autumn".
"This is a bad Bill and if Nick Clegg is serious he must spell out exactly what his bottom line is," he said. "But in truth this is David Cameron's call, not Nick Clegg's."
'Not a marriage'
Asked about the deputy prime minister's remarks, Chancellor George Osborne told the BBC: "I want changes as well to the health bill, so does David Cameron."
The chancellor also insisted the coalition would last for the full five years of this parliament.
"There's a lot of heat in an election campaign but we move on," he said.
"It's not a merger or a marriage between two political parties. There's nothing wrong with both parties expressing their own individual identities but also coming together to solve these big national problems we've inherited."
Dr Fox told Sky News he had always found Mr Clegg "extremely straightforward to deal with" and did not anticipate any confrontations with him.
"I don't think his style of politics is to demand concessions. It will be to look to the coalition agreement and over time to show that there has been success in bringing the programme together."
But Labour leader Ed Miliband told the BBC Lib Dem ministers should demand a change in direction from the government, or leave.
"What I say [to them] very clearly is, 'You're being led by the nose by a Conservative government... and frankly, if I was in your position and I didn't get that change in direction then I wouldn't stay in this government."
Mr Clegg dismissed Mr Miliband's remarks and said the Labour leader had offered no real alternative to the government's economic policies.
Asked whether he could ever envisage joining the Conservatives, Mr Clegg appeared shocked, and said: "No, never. I am not a Conservative - never have been, never will be. Never, never, never.
"I will be carried out in my coffin as a card-carrying Liberal Democrat."
In Thursday's election, the Conservatives, who already controlled more councils than all the other parties put together, increased their number of councillors and gained control of two councils.
Labour made significant gains in town halls in the north of England and in the Welsh assembly elections, where it fell just short of an absolute majority, and held Leicester South in a parliamentary by-election.
In Northern Ireland, the DUP and Sinn Fein won the most seats in the assembly with 38 and 29 respectively.