Cllrs Keith Glazier and Bill Bentley, the Lead Members for Adult Social Care, have added their names to a letter published in The Times newspaper on February 10, raising concerns about how plans for free home care will be paid for.
The letter was signed by more than 75 council bosses in England responsible for adult social care.
This was discussed at the full council meeting on February 9 and afterwards Cllr. Glazier said, "We fully support the principle of providing support to those who have critical care needs.
"But this Bill is unclear and unfunded and could force us to make cuts to other services to pay for it.
"This is a particular concern for us in East Sussex as we have a large elderly population which is growing and it is wrong to raise expectations in this way for some of the most vulnerable people in our society.
"Councillors across all political parties are voicing their concern and we are totally behind it."
The Personal Care at Home Bill is currently going through Parliament following an announcement in the Queen's Speech last year.
Councillors believe the annual costs will be higher than Government estimates. These issues have been raised by the Local Government Association (LGA) and the Association for the Directors of Adult Social Services (ADASS).
Research carried out by ADASS across 61 local authorities show the average cost of care is about £200 per week, substantially higher than the £103 per week Government estimates.
The cost to councils would be about £580m each year rather than the £250m assumed in the proposals.
At the East Sussex full Council meeting it was agreed to set aside £750,000 just for the introduction of the plans although the annual costs could be considerably more.
Councillors are now calling on the Government to commission an independent review of the Bill including an analysis of the financial position.