The government has introduced legislation, due to be debated in the Senate on Wednesday, to deregulate university fees, cut course funding by 20 per cent, increase the interest rate on student loans and expand federal funding to private colleges, TAFES and diploma courses.

The representative poll of 1300 Australians, commissioned by Universities Australia, shows that 59 per cent of Australians oppose the government's reforms with 40 per cent strongly opposed. Only 22 per cent of Australians support the reforms in their current form, with just six per cent strongly supportive.

The release of the poll comes as a Coalition-dominated committee laid the groundwork for one component of the government policy to be softened, urging a rethink of the plan to index student debts at the long-term government bond rate

Universities Australia, the peak body for the university sector, supports fee deregulation but is seeking amendments. On top of calling for the government to peg student debts to inflation rather than the higher bond rate, it wants to reduce the 20 per cent funding cut and fund a structural adjustment package.

When presented with these amendments, voter support for the reforms rose to 56 per cent with only 18 per cent opposed.

Universities Australia chief executive Belinda Robinson used to poll results to urge Senate crossbenchers to strike a compromise deal on the reforms.

In a report released on Tuesday the Senate standing committee on education and employment, dominated by Coalition members, recommended the government's higher education bills be passed with modest changes.

The committee urged the government to explore an alternative hybrid interest rate model proposed by HECS architect Bruce Chapman. Under this model, graduates would pay the higher interest only when they are earning above the repayment threshold (around $50,000). Fairfax Media understands Education Minister Christopher Pyne has been considering this option and would adopt it if it helps secure a Senate deal on fee deregulation.

The government's plan to peg student debts to the long term government bond rate, capped at 6 per cent, is opposed by the entire tertiary sector. Modelling by Professor Chapman has found the government's proposal would hit poor graduates and women with children the hardest because of the extra time they spend outside the workforce.

"[T]he committee believes that the indexation of HELP debt is an area worthy of further consideration to ensure graduates who may not reach their earning potential are not overly burdened by debt," the committee majority report says. "The committee notes that the interest rate on HELP and the conditions of repayment have a significant effect on the size of the debt burden. Therefore, in light of the evidence, the committee urges the government to re-examine this aspect of its reforms."

The committee also called for the government to explore funding a structural adjustment package to help regional universities and others in need adjust to a fully deregulated system. The government should also recoup the debts of students living overseas, it recommends – a call backed by the university sector.

Labor and the Greens wrote separate dissenting reports calling for the government's entire package to be rejected.

On Tuesday Clive Palmer backed away from his earlier suggestions that he was open to supporting the government's changes if it meant the higher fees funded an expansion of student scholarships. Palmer United will combine with Labor and the Greens to block fee deregulation in the Senate, Mr Palmer said.