WASHINGTON—Senate Republicans are citing renewed budget-deficit fears as they pump the brakes on more coronavirus-aid spending, putting them at odds with President Trump’s push for tax cuts and an infrastructure package on top of roughly $3 trillion of funds approved so far.

Many GOP lawmakers, facing pressure from conservative groups, say any new infrastructure spending is a nonstarter. They are also lukewarm on Mr. Trump’s call to slash payroll taxes, paid by workers and employers. Republican leaders have instead prioritized…

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