Both Peter Nutting, Conservative leader of Shropshire Council, and Shaun Davies, Labour leader of Telford & Wrekin Council, said restrictions could go on beyond December 2 – the current date set by government for the end of the planned lockdown.
Parliament will tomorrow vote on whether to bring in the four-week lockdown, which would begin on Thursday.
Councillor Nutting said he was concerned about the impact of the shut-down on the county's businesses and had been pressing Shropshire MPs to lobby for money to support those firms that lose out over the coming month.
During the first lockdown earlier this year the government provided substantial grants which kept many businesses going.
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Councillor Nutting said: "We had a meeting with the Shropshire MPs this morning and asked them to look into what funding is available and just stressed our great need in Shropshire.
"They have extended the furlough scheme which is good but we could do with more money for grants for businesses as the pot we had is now empty."
Councillor Nutting said he hoped that the lockdown would be effective in reducing the number of cases within four weeks, but added that he believed "it will be a bit longer than the four weeks".
Councillor Davies also said he expected lockdown restrictions to go on longer than the planned four weeks "in some form or another".
He said the government's failure to act sooner meant the lockdown would be "longer and harder than it had to be".
The Telford & Wrekin leader added that the government needed to ensure it uses the time afforded by the lockdown well.
He said: "This second lockdown is late coming, just like the first. As a result the lockdown will be longer and harder than it had to be.
"This should not been seen as 'downtime' the government must use this time to fix track and trace and design an exit plan.
"If numbers get right down, and the R number is below one then there is no reason why this lockdown should last a day longer than December 2 – but the government must get grip and focus and develop a package of support to help people help themselves, their families and their communities."
Politicians elsewhere have suggested the country could come out of lockdown for a week over Christmas and then return to strict measures in the New Year.