With the UK's tax burden at an 80-year high and the Conservatives trailing Labour in the polls, they want him to "go much further" in easing the burden on Britons.
The demands came after the Chancellor slashed another 2p off national insurance contributions in yesterday's Budget.
Putting tax at the heart of the looming election battle, Mr Hunt suggested the Tories could even axe the levy altogether.
His intervention part of a package that gives around 500,000 families more child benefit - draws a clear dividing line with Labour.
But with Sir Keir Starmer's party up to 20 points ahead in opinion polls, some Conservatives want the Chancellor to be even bolder.
Former Home Secretary Dame Priti Patel welcomed the national insurance cut, but warned "more work is required" as she pressed for ministers to help firms "benefit from our Brexit freedoms".
She told the Daily Express: "Overall, the announcements by the Chancellor were a welcome move in the right direction.
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