The chancellor, George Osborne, has signalled that the government is to downplay its commitment to Lords reform in response to the coalition parties' losses in the local elections.

He insisted the government was concentrating on the economy and, in an interview on the BBC's Andrew Marr show on Sunday, he repeatedly said that House of Lords reform was not a priority.

Many Tories have blamed Lords reform, and the way it creates the impression that the Liberal Democrats are exerting an undue influence over the government's programme, for the collapse in the Conservative vote in the local elections.

Ministers have already published a draft Lords reform bill and, because of the high level of cross-party opposition to the plan in the Commons and the Lords, and the amount of debating time that has to be allocated to constitutional bills, the issue is expected to dominate the new session of parliament that will start with the Queen's Speech on Wednesday.

But Osborne, in what could be a hint that the government is willing to make concessions on Lords reform in the face of sustained opposition, said that ministers would not allow the issue to take up the bulk of their time.

"I think we do need to focus on the issues that really matter," Osborne said. "We do need to focus on the economy, of course, at a time like this and other issues like welfare and education and healthcare.

"When it comes to the House of Lords, parliament will debate this. Parliament's perfectly capable of debating many things, that's what parliaments do. But it is not going to be the No1 overriding priority of this government – absolutely not."

Osborne said the government was entitled to pursue the issue because all three main political parties proposed Lords reform in their manifestos.

"But it is not going to be occupying the bulk of the time of people like myself, David Cameron, and indeed Nick Clegg," Osborne went on. "We are focused on the really important issues that matter to people watching."

Osborne's comments will reinforce suspicions that the government will eventually concede a referendum on Lords reform. Cameron and Clegg have both said that they see no need for a referendum on Lords reform, because voters backed the idea at the 2010 general election, but Labour are demanding one and, with Tory rebels threatening to support them, ministers may decide that granting a referendum is the only way to get the legislation through the Commons.

In another sign that Conservative ministers in the coalition lack enthusiasm for the plan, Lord Strathclyde, the leader of the Lords, told the Sunday Telegraph repeatedly in an interview that it was possible that Lords reform could be killed off by the Commons.

Osborne told the Marr show that he did not believe that Lords reform or the government's plans for gay marriage were to blame for the local election defeats. In an article published in the Mail on Sunday, referring to the results, he said he was going to "take it on the chin".

He also insisted that, while the budget may have contributed to the Tories' loss of support, the problem was to do with the way it was presented, not with the measures it contained.

"I know the way the budget was presented meant this message wasn't heard," he wrote. "I take responsibility for that. But that doesn't stop the tax cuts from millions of people contained in the budget from actually happening and helping families."

In response to the article, Douglas Alexander, the shadow foreign secretary, said Osborne was missing the point.

"I see George Osborne is apologising for the spin of the budget," Alexander said. "Frankly, he should be apologising for the substance of the budget."