The authority's latest financial strategy has revealed it could be facing a £57 million funding gap by the end of 2025.
But Councillor Peter Nutting said he is expecting more money to come from the government which has not yet been taken into account.
"The reality is that this council is pushed for money but the budget relies on how much money the government sends us," he said.
"At the moment the government is completing a review and they have not decided yet how much is going to local government.
"This is a cold, hard report but we do expect to get some one-off payments though and don't expect to lose anything that we currently get.
"We could be up to £38 million adrift in a couple of years time but if you put in the grants, that brings it to about £10m and I think it could be brought down to £5m or so, so it's important to keep putting pressure on the government."
Councillor Nutting also said the council has about £100m from assets that can be unlocked in the future.
He expects the proposed Oxon Link Road project to release about 100 acres of development land which is worth about £30m, and land on the outskirts of Oswestry which could generate £6m.
Shropshire Council expects to spend £605.53m in the coming 12 months which exceeds the total funding anticipated of £575.46m - leaving a funding gap to be resolved.
Almost £19m of savings across all areas of the council have been proposed in a bid to produce a balanced budget in 2020/21, but it is anticipated that the funding gap will increase each year over the next five years unless additional funding or savings can be identified.
The report was discussed and approved by full council at Shirehall on Thursday, despite serious concerns from opposition councillors.
Leader of the Lib Dems, Councillor Roger Evans, said the budget is a "mess", while Councillor Pauline Dee said she "shudders" at the savings that will need to be made over the coming years.
Labour leader Alan Mosley added: "This budget is a disgrace and an insult to the people of Shropshire and should be rejected. Local government is in an appalling state and our county is in an appalling state too. We're relying on things that are a wing and a prayer. I fear for the future of our county and our services."