One of Connecticut’s largest public employee unions is trying to rally support in the waning days of the General Assembly session for a study of whether state government should offer a retirement plan to private citizens.

But one of the key lawmakers behind the proposal conceded late last week that the chances of passage this year are poor with the legislature scheduled to adjourn in less than two weeks.

“I think it’s very slim it is going to happen this year, but it is still a very good idea,” Sen. Edith G. Prague, D-Columbia, co-chairwoman of the Labor and Public Employees Committee, said Thursday.

But if the bills should die this year, the concept likely won’t go away, Prague added. “So many folks are struggling to get by with just their Social Security,” she said.

Both the labor panel and the Committee on Aging raised bills that would mandate a study of whether state government should offer a retirement plan to the increasing number of people whose employers don’t provide a pension or a 401(k) savings program.

Council 4 of the American Federation of State, County and Municipal Employees, one of the leading groups advocating for the bill, has argued that two of the three tiers of the traditional American retirement income plan — personal savings and an employer-sponsored retirement plan — are missing from many households. And Social Security simply isn’t sufficient, advocates of the bill say.

About 61 percent of employers nationwide sponsored plans in 2000, but just 53 percent did by 2010, according to the Schwartz Center for Economic Policy Analysis in New York. Over the same period in Connecticut, the percentage dropped from 64 percent to 58 percent.

But the state’s chief business lobby, the Connecticut Business and Industry Association, opposes the study, arguing it would harm the private financial services industry and expose taxpayers to financial risks.

“If the state goes down that road, it needs to be ready to absorb the fiduciary responsibilities,” said CBIA Associate Counsel Eric George, who added that not only includes the costs of administering private citizens’ investments, but covering any penalties should funds be mishandled.

“We already have a private market that services (retirement planning,) and by all accounts, very efficiently, George said, adding that a state program for the private sector might ultimately lead to job losses in the financial services community.

But Teresa Ghilarducci, a labor economist and pension expert with the New School for Social Research in New York, said the same argument was used during the 1930s in a failed effort to block enactment of the Social Security Act.

Ghilarducci, who visited the Capitol Thursday with Council 4 representatives to advocate for the study, said a state-run investment plan ultimately would bolster the private financial services sector, just as Social Security did nearly 80 years ago.

“When more people begin to save for retirement, even a little bit, they become more aware and it increases the overall demand for retirement security,” she said.

Ghilarducci also rejected the argument that state taxpayers might be saddled with paying penalties stemming from potential misuse of retirement dollars. “It happens all the time in the private sector, but there is no incentive for that in a state plan,” she said. In the private sector, “the loyalty of the fiduciaries is to the firm and the shareholders who stand to profit.”

And because Connecticut government already invests a huge pot of money annually — more than $25 billion in assets tied to pension programs for state employees and for public school teachers — it has the ability to manage a more diverse investment portfolio, Ghilarducci said.

Under the proposed legislation, an 11-member task force would study the availability of retirement plans and trends in retirement savings, as well as the projected needs of future retirees.

The study panel would include representatives from the governor’s budget office, other constitutional officers, the state Commission on Aging and experts in the field to be appointed by legislative leaders and Gov. Dannel P. Malloy.