Joe Hockey.

Treasurer Joe Hockey is under pressure to explain contradictory cuts and spending in the budget. Photo: Brendan Esposito

The Abbott government is under pressure to explain contradictory budget cuts in the same portfolios in which it announced eye-catching new policies.

Several contradictions ''hidden'' in the fine print of the budget papers will be raised in Senate estimates hearings and other forums this week.

Universities Australia chief executive Belinda Robinson says the government's much lauded $20 billion medical research fund is a fine idea, but says it is undermined by cuts in other areas of research.

Ms Robinson said some of these other cuts are likely to deter Australians from training as researchers and pursuing PhD and masters level research.

The Abbott government is introducing new fees for PhD students to compensate for millions of dollars in cuts to the $677 million Research Training Scheme.

Ms Robinson says these and other changes to higher education, including higher HELP interest rates changes and government cuts, will ''serve as a major disincentive to those contemplating a research degree''.

Education Minister Christopher Pyne rejected the criticisms, saying the government was providing ''strong support'' to research, including through $150 million for research infrastructure and 100 four-year research fellowships each year.

''Universities can provide scholarships to PhD students if they choose to do so,'' Mr Pyne added.

In other clashing budget measures, the Abbott government is freezing funding for the $160 million ''family relationships services'' programs, while simultaneously Social Services Minister Kevin Andrews has been promoting his $20 million ''relationship vouchers'' policy.

The Coalition is also freezing and culling existing cyber safety programs while simultaneously introducing a new $10 million e-safety program.

Labor's social services spokeswoman Claire Moore said she was concerned about the indexation freeze – which amounts to a cut – to ''family relationship services'', adding that the programs provide ''a really valuable service to parents and children who are at their most vulnerable''.

Family relationship services include support services for families experiencing difficulties, counselling and children's contact services.

Senator Moore also questioned why programs that showed ''no evidence of any problems'' were suffering and said she did not believe initiatives such as the relationship counselling vouchers would adequately compensate.

Mr Andrews said the Coalition had frozen the ''family relationship services'' program to ''help repair the budget left in such a mess by the former Labor government''.

Mr Andrews' $20-million relationships vouchers trial will run for a year, giving as many as 100,000 couples a $200 voucher for relationship education and counselling.

Another to face questions this week about funding freezes is Paul Fletcher, the parliamentary secretary to the Communications Minister.

The Abbott government is pausing indexation and culling cyber-safety programs, after declaring them to be areas of particular interest to the government.

While cutting these programs the government is simultaneously injecting $10 million of new money for children's online safety, including the establishment of a Children's E-Safety Commissioner.

Shadow minister for communications Jason Clare criticised the ''hidden cuts'' as part of the wider ''budget of broken promises''.

A spokesman for Mr Fletcher said the funding freezes and program culling would allow for ''greater efficiency'' and less duplication with the Commissioner acting as a central authority overseeing online safety.

''A public consultation paper . . . noted that there are a range of existing Australian government online safety resources and programs which could be transferred to the Commissioner's control,'' he said.

''The clear policy intent of the government is to have a single organisation which takes the lead in relation to online safety for children.''