Prime Minister Tony Abbott faces a fresh threat to the abolition of the carbon tax, with two key crossbenchers warning that if the government continues to pander to Clive Palmer it risks losing their support.

NSW senator David Leyonhjelm and South Australia's Bob Day issued the stern warning on Saturday, saying they were concerned that ''severe compliance'' obligations placed on business by Palmer United Party amendments to the carbon tax repeal bills could be ''worse than the tax itself''.

Family First Senator Bob Day and LDP Senator David Leyonhjelm. Credit:Alex Ellinghausen

Senator Leyonhjelm told The Sunday Age: ''We are signalling to the government they don't have a blank cheque with us. If you give too much ground to PUP you might lose us. We want to see the carbon tax removed, but not at the price of some big brother obligation that makes life difficult for industry.''

Amid chaotic scenes in the Senate last week, as the government tried and failed to deliver the long-promised repeal, Coalition Senate leader Eric Abetz was able to count on the votes of Senator Leyonhjelm, who represents the anti-tax Liberal Democrats and Senator Day of the socially conservative and economic dry Family First.