Tony Abbott’s office took quite a while to respond to Sky News’ Wednesday report that a group of backbenchers from across the parliament planned to bring forward a same-sex marriage bill on August 11, with the party room considering a week later whether Liberals should get a conscience vote.

When a statement finally came – from a spokesperson – its tone was a very cold putdown of those promoting the bill.

“Any member can introduce a private members’ bill into the parliament but they do not come before the joint party room for discussion unless they will be voted on in the parliament. It is rare for a private members’ bill to be voted on and any bill would be subject to the usual process,” it said.

“The prime minister’s position remains the same as it has always been and he supports the current policy that marriage is between a man and a woman. The government’s priority is strong economic management and keeping Australians safe.”

The leak caught a number of the bill’s sponsors as well as Abbott by surprise. The face of Abbott’s chief of staff Peta Credlin is said to have become a storm cloud when she heard of the Sky story, although it was known there were cross-party talks for a move in the spring session. Cabinet minister and Leader of the House Christopher Pyne has been the liaison between the group and Abbott’s office.

Now the issue looms as a major management problem for Abbott. He’s caught between the conservative supporters on whom he depends and a swell of feeling among many Liberals that same-sex marriage should be embraced for reasons of both principle and electoral pragmatism.

Abbott’s sister Christine Forster, who a few days ago lobbied those at the Liberal federal council on the issue, welcomed the bill. “I’m very hopeful our federal parliamentary party members will take the view that this is a matter of conscience that should be decided by our elected representatives,” she said. The latter point is rejecting the call by some Liberals for a plebiscite.

The proposed bill is to be moved by Queensland Liberal Warren Entsch and seconded by Labor’s Terri Butler, with other sponsors being Liberal Teresa Gambaro, Labor’s Laurie Ferguson, independents Cathy McGowan and Andrew Wilkie, and the Greens’ Adam Bandt.

It is believed the drafting was undertaken by Gambaro and the negotiations for sponsors were conducted by Entsch. Ministerial supporters Malcolm Turnbull, Simon Birminghan and Marise Payne have seen the bill.

Butler looks forward to seconding the bill, but warns its “only chance of success is if the Liberals and Nationals have a free vote”. Gambaro called for the issue to be dealt with “carefully, responsibly and in a respectful manner”.

Entsch is annoyed at the leak. “I have been saying there would be a bill in the spring session,” he said, speaking from Vietnam. “I’m going to deal with it in the parliament, not the media,” he added, warning that discussion during the recess could just endanger its chances.

During the last parliamentary session Abbott dismissed a Labor bill and suggested the only way to go was a cross-party one. He said same-sex marriage was an important issue and “if our parliament were to make a big decision on a matter such as this, it ought to be owned by the parliament and not by any particular party”.

But Abbott sounded grumpy in the last few days when asked about same-sex marriage in the wake of the US Supreme Court decision upholding same-sex marriage under the American constitution, which has given momentum to the push in Australia.

In recent weeks the word has been that Abbott wants to bury the issue for the rest of this year, which would then enable him to argue that it was too late to have a vote before the election.

The right is bringing massive pressure to bear and has various strategies open to it to either head off or defeat a conscience vote.

It could move for a partyroom vote to affirm the present policy on marriage – that it should be only between a man and a woman. A win on that would likely overtake the question of a conscience vote.

The issue could be taken to the Coalition partyroom – referred to in Abbott’s Wednesday statement -–rather than the Liberal partyroom. That would strengthen the numbers against a conscience vote.

Or Abbott could simply try, as implied in his statement, to tough out the situation and suppress the bill.

Whichever way Abbott turns there will be hazards. For a majority of Australians the question of legalising same-sex marriage is a no-brainer. For Abbott, it is a no-win situation.

Listen to the Politics with Michelle Grattan podcast, with Labor environment spokesman Mark Butler, here or on iTunes.