A fightback by Nick Clegg ran into trouble on Tuesday when the deputy prime minister faced Tory and Labour hostility bordering on contempt in both houses of parliament as he vowed to push through an elected second chamber by 2015.

In a sign of the bruising battle awaiting Clegg as he seeks to rejuvenate his Lib Dem leadership after an overwhelming defeat in the alternative vote referendum, the Tory cabinet minister charged with selling the Lords reform plans cast doubt over the deputy prime minister's timetable.

Lord Strathclyde, who has privately left Tory peers in no doubt of his scepticism about Clegg's plans to ensure that at least 80% of the upper house is elected, indicated that a parliamentary bill may not be introduced before the next general election. "If a bill came forward, it would be a government bill and it would be treated as such," Strathclyde said, appearing to cast doubt on the timetable.

The intervention by the leader of the Lords, who joked with Tory peers as they tore into Clegg's plans during an hour-long statement in the upper house, flew in the face of a commitment from David Cameron at Tuesday's meeting of the cabinet. The prime minister, who said before the election that he regarded Lords reform as a third-term priority, was strongly supported by George Osborne as he said he wanted to see the first elections to the reformed upper house by 2015. Cameron demonstrated his support for Clegg by sitting at his side in the Commons as the deputy prime minister unveiled his plans, which contained two key elements:

• A draft House of Lords reform bill that would slash the membership of the upper house from 789 to 300, of whom 80% would be elected by proportional representation via the single transferable vote. Members would each be eligible for a single term of 15 years on a non-renewable mandate.

The elected peers would be phased in though three tranches starting in 2015, with 100 peers elected on each occasion. The 80% figure is a compromise between the Lib Dem manifesto, which called for a "fully elected" second chamber, and the Tory manifesto, which called for a "mainly elected" one.

• A white paper containing proposals for a 100% elected upper house, the Lib Dems' preferred option. This is designed to win support from Labour, which called in its manifesto for a "fully elected second chamber", to be introduced in stages.

Clegg, who promised that both proposals would be scrutinised by a cross-party committee of MPs and peers over the next year, said: "The prime minister and I are clear – we want the first elections to the reformed upper chamber to take place in 2015. But, while we know what we want to achieve, we are open-minded about how we get there. Clearly our fixed goal is greater democratic legitimacy for the other place but we will be pragmatic in order to achieve it."

He pointed out that all three parties had backed a wholly or mainly elected Lords and claimed he would use all the legislative tools at his disposal to realise the manifesto commitment of all three parties.

Clegg's remarks suggest he wants to whip the changes through parliament and is willing even to use the Parliament Act of 1949, which would allow the government to force through a bill against opposition from the Lords. A previous judicial ruling in 2005 by Lord Phillips of Worth Matravers suggested the use of the parliament act may be constrained, on fundamental constitutional changes, indicating the plans could become bogged down in the courts.

But Clegg struggled in the Commons to win any support for his reforms from Tory MPs, many of whom regard the plans as irrelevant, time-consuming and from the same political stable that proposed the disastrous AV referendum. One Labour MP, David Winnick, said he had never seen a government proposal met with less enthusiasm from its own side. The shadow justice secretary, Sadiq Khan, described the plans as an anti-climax, and said it would be wrong to introduce the reforms without a referendum. Khan won cheers from Tory MPs when he said: "These proposals risk being a dog's dinner with nobody happy at the outcome, not even the Lib Dem activists he is trying to appease."

A succession of Conservative MPs challenged Clegg. Bernard Jenkin said the plans came from the same discredited roadshow that had brought he referendum on AV.

Clegg himself produced cheers on the Commons benches when he admitted his plans were not top of the public's concerns. He said a more democratic second chamber would help improve constituents' practical concerns, such as schools and hospitals.

The deputy prime minister, who had hoped to complete the unfinished business of the 1911 Parliament Act, which first raised the prospect of an elected upper house, admitted he had needed to dilute his plans. "Personally I have always supported 100% elected but the key thing is not to make the best the enemy of the good," Clegg said. "That approach has stymied Lords reform for too long. Surely at the end of the day we can all agree that 80% is better than 0%."

Strathclyde expressed strong support for the reforms as he repeated Clegg's statement in the Lords, but then delighted Tory sceptics as he joked he was no expert on PR elections, adding that Clegg was "very keen" on the idea. The Lords leader appeared to set himself at odds with Clegg by declining to say whether an elected chamber would be an improvement. "Would it make things better is a good philosophical question which is very hard to answer. I dare say some things might be better, some things might be worse," he said. "But overall when the second chamber took a decision with the backing of the electorate, that would be more authoritative."

Strathclyde indicated that the joint committee that will examine the proposals would be in no rush. "I hope it will do so in a most realistic way. Everything that I have heard this afternoon leads me to believe that the joint committee will have plenty of work to do," he said.

The cross-party attacks on Clegg's plans, which follow Cameron's declaration that he will take the lead on amending the government's NHS reforms, will raise questions about the deputy prime minister's ability to rebuild his party after the Lib Dems' electoral setbacks.

The former Lib Dem cabinet minister David Laws, meanwhile, has warned his party not to risk wrecking the coalition by sniping at the Conservatives.

In comments that will be seen as a warning to ministers such as Chris Huhne and Vince Cable, who have gone public with criticisms of Tory colleagues, he told the Times: "We could get our way over one or two key issues by storming off, voting against them, briefing against them, whatever. But when the next key issue is on the table and we need the co-operation of everybody in the coalition, will we get it? Maybe we won't."

Laws, who was barred from the Commons for seven days from Monday over revelations about his expenses claims, said: "We shouldn't be sitting around in the corner of the political room sulking about the fact that we are in government and looking forward to the opportunity when we can return to the splendid irrelevance of opposition."