The federal government faces a new hurdle in the Senate, with Family First and the Liberal Democratic Party forming a new voting bloc.

David Leyonhjelm, the NSW senator-elect representing the Liberal Democrats, has revealed he would vote in alliance with South Australia's Bob Day of Family First when the new Senate sits from July 1.

Prime Minister Tony Abbott and Treasurer Joe Hockey face more senate hurdles. Credit:Andrew Meares

They have agreed to vote together on all economic issues, but will decide their own positions on social issues. As a self-described libertarian, Mr Leyonhjelm supports same-sex marriage, for example, whereas Family First is opposed to it.

The two-member bloc is half the size of the Palmer United Party-Ricky Muir alliance, but is likely to provide some headaches for the government as it seeks backing for its legislative agenda, particularly if that involves any new taxes.