One of the Government's newest - and arguably one of its most influential - senators is calling for the GST to be increased and broadened, the abolition of the federal health and education departments and the privatisation of the ABC if it fails to address concerns of left-wing bias.

In his maiden speech to Parliament, Senator James McGrath, who has previously been a Liberal party strategist, has also demanded the ABC's youth radio station triple j be privatised immediately.

But it is his call for dramatic changes to taxation that is likely to trigger the most reaction from opposition parties.

"Taxes on jobs and productivity such as the payroll tax and company tax must be abolished and reduced respectively," he told the Senate.

"To cover the states from loss of income from payroll tax, the GST should be broadened to cover everything and the GST should also be increased to 15 per cent.

"Of course there should be compensation for the less well-off and income tax cuts."

Senator McGrath, a former deputy federal director of the Liberal Party, has also argued in favour of axing key federal departments in a bid to encourage smaller government.

"Bureaucracies have become more bloated, more process-driven and more out of touch," he said.

"I'm calling for the abolition of the federal departments of health and education, with universities also to be run at a state level."

The Queensland senator also spoke out against compulsory student unionism, which currently forces all university students to pay a fee to support the student organisation at their institution.

He says he will introduce a private member's bill to abolish the current system and bring in voluntary student unionism.

"Students like anyone should have the freedom to decide themselves whether or not they join a student body or union," he said.

Senator calls for ABC sale if bias concerns not addressed

On the ABC, Senator McGrath is also calling for a review of the public broadcaster's charter, claiming its sole representation of "inner-city leftist views" has left him and other constituents behind.

His comments come at a difficult time for the ABC, which has announced the axing of 80 jobs as a result of the Government's decision to abolish the $220 million Australia Network.

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"As someone who grew up in regional Queensland, I grew up with the ABC but the ABC has left people like me and my constituents behind," Senator McGrath told Parliament.

"I want to support the ABC. I like the ABC.

"Yet while it continues to represent only inner-city leftist views, and funded by our taxes, it is in danger of losing its social licence to operate."

He says if the ABC fails to make "inroads to restore balance" then it should be sold and replaced by a "regional and rural broadcasting service".

But Senator McGrath says an earlier sale can be made with triple j, arguing the youth station is popular enough to stand on its own two feet in the commercial sector.

"Triple j, because of its demographic dominance and clear ability to stand on its own, should be immediately sold," he said.

Senator McGrath is seen as an influential figure in the Liberal National Party, having successfully directed the 2012 election campaigns for the conservatives in Queensland and the Northern Territory.

McGrath joins other Liberals in criticising ABC

The Government is yet to unveil the results of its efficiency review into the ABC and SBS, which Communications Minister Malcolm Turnbull says has identified significant "back of house" savings.

Prime Minister Tony Abbott promised the night before the election there would be no cuts to the ABC or SBS.

But in the budget the Government imposed a 1 per cent efficiency dividend which it said at the time would be a "down payment" on further cuts stemming from the efficiency review.

Since the election, several Liberals including the Prime Minister have voiced their concerns about what they say is the ABC's bias and dominance of the Australian media landscape.

In February, Mr Abbott criticised the ABC for publishing intelligence leaks obtained by the former US National Security Agency contractor Edward Snowden.

The Prime Minister said the ABC "instinctively" takes everyone's side "but Australia's".

He also questioned the need for the ABC's Fact Check unit.

It followed months of internal pressure from Liberals who had called for the ABC's funding to be cut.

Liberal senator Cory Bernardi has previously called for the ABC's digital expansion to be curtailed, saying it has resulted in the "cannibalisation of commercial media".