Joe Hockey’s second budget may have won an initial round of applause from voters but that does not mean it will get an easy passage through parliament.

A clutch of crossbench senators will likely hold sway on whether key items such as the treasurer’s childcare package and pension reform will get across the line.

Heading into a sitting fortnight for the House of Representatives, Prime Minister Tony Abbott is urging the Labor Party to ‘work with us’ in backing the $20,000 instant asset write-off for small business when budget bills start to be debated.

‘We all know that the Labor government got us into a mess,’ he told reporters in Brisbane on Sunday. ‘This is a chance for the Labor Party to be part of the solution rather than the problem.’

But Opposition Leader Bill Shorten still believes it is a ‘sneaky’ budget that repackages last year’s poorly received effort for opinion polls.

Senators will be going through the budget with a fine toothcomb during two weeks of grilling government departments in Senate estimates.

Two key crossbench senators are not happy the government is sticking with last year’s cuts to family tax benefits to help pay for its new childcare package.

South Australian independent Nick Xenophon believes that while there is a lot of merit in the package, cutting benefits once a child turns six is ‘not a good way to negotiate’.

Tasmanian independent Jacqui Lambie describes it as holding the parliament to ‘ransom again’.

But she does support ending ‘double dipping’ in the commonwealth’s paid parental leave scheme, even though she is yet to be convinced about the latest changes to the pension and is due to meet with Social Services Minister Scott Morrison on Monday.

‘I want to see it all in black and white … I’m still sitting in the middle on that,’ she told Sky News.

Greens deputy leader Scott Ludlam says he is ‘cautiously supportive’ of some of the pension measures but he is arguing for a broader retirement income review.

‘The elephant in the room is superannuation and its tax treatment,’ he told Sky News.

Liberal Democrat senator David Leyonhjelm has broader concerns, like bringing the budget back to balance.

‘There just seems to be this denial that we can spend more than we bring in,’ he told Sky News.