This time of year, nothing expresses disappointment with state policy like a lump of coal.

A group of more than 40 union janitors, protesting the impending loss of their children's health care coverage, attempted to deliver a 2-gallon bucket of coal to Gov. M. Jodi Rell at the state Capitol this week.

Drumming plastic pails and marching in a circle, the janitors — led by Wojciech Pirog, a union delegate dressed as Santa Claus — chanted "Hey, hey, ho, ho, health care costs have got to go," in front of the Capitol Monday afternoon.

Because of an increase in the cost of health care premiums, which goes into effect Jan. 1, more than 350 janitors' children and 68 spouses will lose their health care coverage on that date, according to Service Employees International Union, Local 32BJ, which represents about 600 janitors who clean state-owned buildings.

The union says state agencies, which contract with private companies, are not paying those contractors enough to provide health care benefits for workers' dependents.

Workers employed by private contractors hired by the state are subject to Connecticut's standard wage law, under which they receive benefits equal to 30 percent of their wages. For example, a janitor who earns $12 an hour, is entitled to about $3.50 an hour worth of benefits, said Kurt Westby, union president of Local 32BJ.

Currently, it costs $3 an hour to provide an employee, a spouse and dependents with health care coverage. On Jan. 1, the cost rises to $3.50 an hour, Westby said — leaving no room for other benefits.

"You've got to cut something, so you cut the kids off," he said. "Hopefully they go to HUSKY."

"A few hundred thousand dollars could save taxpayers millions of dollars. Adding those children to the publicly funded HUSKY program will cost more than $2 million."

During the coming legislative session, the union plans to lobby for a bill that would require the state to make up the shortfall and pay the difference.

The governor's office refused to accept the bucket of coal, but allowed Flor de Maria Matos, a union janitor, to deliver a letter to her Capitol office. Chris Cooper, a Rell spokesman, accepted the letter on behalf of the governor.

"This issue, because it involves a budget issue, will be a topic of the budget discussion," Cooper said. "In this environment, I think it will be difficult to advance programs that have additional costs."

The dispute is one of countless conflicts bound to arise over state spending in the coming months, as state government grapples with a shortfall that, by some measures, could reach $6 billion over three years — at a time when few public officials want to raise taxes.

"The governor has turned a blind eye to the health care needs of the very workers who clean her office," Westby said. "These are state workers that are going to lose benefits, but because they happen to work for state contractors, it's easier for the state to ignore them."