Liberal Democrat leader Nick Clegg has said the idea of tax breaks for married couples is wrong, and would not work.
The deputy prime minister told Sky News there were "philosophical differences" with the Lib Dems' coalition partners, the Conservatives, over the issue.
He said there was a limit on what the state "should seek to do in organising people's private relationships".
Fellow Lib Dems Vince Cable and Simon Hughes also attacked the idea during interviews with the BBC.
Mr Hughes, deputy Lib Dem leader, also denied the issue showed coalition tensions, telling BBC Breakfast it was one of four areas in the coalition agreement where the two parties had agreed to differ.
The other areas were nuclear power, nuclear energy and tuition fees, he said.
'1950s model'Conservative leader David Cameron said in his party conference in October: "Marriage is not just a piece of paper. It pulls couples together through the ebb and flow of life.
"It gives children stability. And it says powerful things about what we should value. So yes, we will recognise marriage in the tax system."
Conservative backbenchers are pressing for their party's election pledge to introduce transferable tax allowances worth up to £150 a year to be implemented during the current parliament.
Mr Clegg told the Dermot Murnaghan programme he was in favour of marriage, but said children "thrived best when they see their parents happy together", whether they were married or not.
He said that he did not think the state offering people "20 quid back would make much difference to people's decisions" on whether or not to get married.
Business secretary Vince Cable told BBC One's Andrew Marr Show that he was a big believer in marriage personally, and also rejected the suggestion Mr Clegg had brought up the subject as a "gratuitous" bit of coalition politics.