The economic crisis engulfing the coalition deepened after the Tory head of local government raised the spectre of councils across England and Wales running out of cash reserves used to boost local economies within five years, under the weight of massive spending cuts.

The warning from Sir Merrick Cockell, chair of the Local Government Association and leader of Kensington and Chelsea council, amounts to a plea to the chancellor, George Osborne, to hold off from further savage cuts on local authorities this autumn.

Meanwhile, in an other sign of internal Tory dissent over economic strategy, former minister David Davis will question Osborne’s strategy on Monday.

At the start of a week in which David Cameron will try to steady Tory and Liberal Democrat nerves with a reshuffle, and Osborne will announce measures aimed at boosting job creation and growth, the LGA intervention echoes a growing view among Tories that austerity alone will not pull the country out of recession.

At present councils hold £17bn of reserves – money set aside mainly to fund local, job-creating infrastructure projects, but also to meet unexpected costs such as redundancy payments.

Ministers including community secretary Eric Pickles have, however, put councils under heavy pressure to raid their reserves to offset the effect of 28% funding cuts from Whitehall, so they can maintain levels of local services. Pickles has said that when times are hard, councils must not turn their cash vaults into “Fort Knox”.

Hitting back at such an approach as short-sighted and self-defeating, the LGA is now insisting that it would wipe out council reserves within five years and leave local authorities with nothing to spend on vital job-creating infrastructure schemes that are the means of pulling the economy round.

Cockell told the Observer that eating up reserves would destroy the capacity of local government to address local needs. He said: “Councils are working hard to shield frontline services from the 28% cut to the money they receive from government. But cash reserves can only dampen the impact, not fill the gap. If councils plundered their reserves to cover the cuts, the cupboard would be bare within five years and there would be nothing left to invest in the growth-promoting projects Britain needs.”

Borrowing a phrase from Osborne’s critique of Gordon Brown’s government, he said that councils had “fixed the roof while the sun was shining, which is why they are now in a position to invest in the infrastructure and development projects which will help drive Britain out of economic downturn”.

He added: “As with any prudent family budget, councils set aside money to invest for the future and hold some back for a rainy day. Similarly, a well-run business will keep at least six to eight weeks’ outgoings in reserve. Council reserves cover exactly that. If the banks had taken a similar approach we wouldn’t be in the mess we are.”

Ahead of a speech calling for an “alternative” pro-growth strategy, former Tory leadership challenger Davis criticised Osborne for blaming Britain’s economic woes on Europe’s debt crisis. He told the Sunday Telegraph that deeper spending cuts were now “inevitable” before the next general election. “The coalition’s cuts should have been earlier and deeper,” he said. “This is not about individual policy areas. This is about something more fundamental … something deeper. There is an alternative economic policy.”

Osborne, who will retain his post in the reshuffle, is expected to begin a week of announcements aimed at boosting growth. They are likely to include new measures under which government will underwrite local housebuilding projects and new plans to improve lending to small businesses.

Tory MPs have become increasingly impatient to see a new growth strategy to complement austerity. Bernard Jenkin, chair of the Commons public administration committee, said: “This government has so far shown an extreme lack of urgency about the economy. It cannot be politics as usual. We must reduce the tax burden and regulation on business while sticking to the deficit reduction, or cutting even deeper.”

The reshuffle is likely to see an emphasis on the promotion of ministers with business interests and expertise. Grant Shapps, the housing minister, is tipped for promotion to the cabinet, perhaps as party chairman, as is Chris Grayling, the employment minister, who only narrowly missed out on a cabinet post in 2010. Sir George Young, leader of the House of Commons, and Patrick McLoughlin, the chief whip, are thought most likely to leave the cabinet.