Shrewsbury mayor Alex Wagner said if the town council did not “step up” and take on this work, it faced “a further visible decline in local services”.
Shropshire Council has been forced to cut costs to balance its budget and avoid the possibility of effectively going bankrupt.
“Local government is changing,” the Lib Dem councillor said.
The question, he continued, was whether that change was managed locally “in Shrewsbury’s interests,” or whether to “allow decisions elsewhere to dictate a slow decline in the services people see and rely on every day”.
Other councils, including Oswestry, Ludlow and Broseley, also plan to increase taxes to pay for the extra workload.
Last month, a Lib Dem town councillor in Oswestry quit the party over the policy.
He said it was unfair to charge people a second time for services which they were already paying Shropshire Council for.
If Shrewsbury Town Council’s budget proposals are approved by councillors, the authority will see its income through the tax precept rise from £2,389.595 to £4,816,178.
In its draft budget, Shrewsbury town council said it was preparing to hire nine full time staff, buy a 15-tonne road sweeper and a 3.5-tonne road sweeper, among other equipment.
Wagner and the town council pointed to a survey of people in the town which found 71% supported the town council taking over street sweeping and litter picking.
Of the 1,200 people who replied, 79% also agreed that protecting key local services was important, even if it costed more.
A full meeting of the town council will discuss the budget proposals on 26 January.