Connecticut is one of 13 states that taxes seniors’ Social Security income, a practice Democratic and Republican lawmakers alike are hoping to end.

More than a dozen bills have been introduced this year that seek to exempt all Social Security income from Connecticut’s personal income tax.

Under current law, single taxpayers’ Social Security income is exempt from tax if his or her federal adjusted gross income is less than $50,000; married couples filing jointly are exempt from taxation of their Social Security if their adjusted gross income is less than $60,000, according to the state Department of Revenue Services. The exemption costs the state about $79 million a year and benefits 320,000 tax filers, according to the Office of Fiscal Analysis

For those with income that exceeds those limits, Social Security income is taxable, putting a financial strain on many Connecticut seniors, Sen. Gayle Slossberg, D-Milford, said.

“We have a lot of seniors who are on the edge and they’re struggling,” she said. “Everywhere I go I (hear from) seniors who are struggling. It’s definitely something people mention to me.”

The pitch is similar to one made by Republican gubernatorial candidate Tom Foley in the final weeks of the 2014 campaign. Foley estimated that it would cost the state an additional $40 million a year to exempt the rest of Social Security benefits from the state income tax.

Nearby states including Massachusetts, New York and Maine exempt all Social Security income from taxes and “it’s time for us to have a conversation” about making changes in Connecticut, Slossberg said.

But the bill has been introduced at a time when the state is trying to combat declining revenues, meaning it likely will face an uphill battle, according to Rep. Jeffrey Berger, D-Waterbury, who co-chairs the legislature’s Finance, Revenue and Bonding Committee.

The bill introduced by Slossberg and Rep. Kim Rose, D-Milford, was referred to the committee soon after being introduced. It’s one of several bills introduced early in this legislative session that aim to reduce taxes, including proposals to exempt diapers from state sales tax, reduce the gas tax, phase out the real estate conveyance tax and repeal the business entity tax, among others.

With an eroding revenue stream it will be “very, very difficult” for the Finance committee to consider proposals that would further reduce the state’s income, Berger said. To stand a strong chance, bills need to be revenue-neutral or have a “minimal” impact, costing the state $100,000 or less, he said.

There is not yet an analysis of how many seniors would be affected by exempting Social Security income from taxes or what it would cost the state, Slossberg said.

She acknowledged the difficult financial climate in which the legislature is making decisions.

But there are other options to consider, she said, besides exempting Social Security income outright. Some states have raised the income threshold cut-off. Connecticut could, for example, change and begin taxing couples who earn $100,000 or more in income.. Another option some states have adopted is exempting certain seniors from the tax based on their age, she said.

“If we have a productive conversation, that’s a step forward. We need to start the conversation somewhere,” she said. “Our seniors need help.”

While the bill pertains to the state’s income tax on Social Security benefits, some seniors also pay federal taxes on those benefits.

In 2012 Social Security beneficiaries nationwide paid a total of $45.9 billion in federal income taxes on their benefits, according to AARP. That figure, the most recent one readily available, included $23.7 billion that went into the Social Security Trust Funds that pay benefits and $18.6 billion that went to the Medicare Hospital Insurance Fund, according to AARP.

Seniors typically have to pay federal income taxes on benefits only if they have other substantial income, like wages, self-employment, interest or dividends, according to the Internal Revenue Service.