The District’s health exchange has a problem — a big money problem.

Like the 14 states that started online marketplaces, the District faces a year-end deadline to prove its Web site can move past technology glitches to meet the next looming challenge in President Obama’s Affordable Care Act: financial self-sufficiency.

But unlike the others, the city does not have enough customers buying insurance on its Web site to copy the funding scheme adopted by most states and the federal government: a tax of a few percentage points on premiums.

To cover its $28 million annual budget, the District’s exchange would have to levy a whopping 17 percent tax on every health plan sold on its Web site.

As an alternative, Mayor Vincent C. Gray (D) on Tuesday will ask the D.C. Council to approve legislation granting the District’s exchange board broad new power to tax any health-related insurance product sold in the city — regardless of whether it’s offered on the exchange.

If Gray and exchange officials get their way, D.C. would fund most of its exchange through products not eligible for the exchange, adding a 1-percent tax on more than $250 million in insurance premiums paid annually by hundreds of thousands of D.C. residents.

Those plans include long-term care, disability, vision, dental, hospital indemnity, and dozens of other health-related policies.

In warnings to city exchange officials in recent months, insurers have threatened that the costs will be passed on to D.C. customers and that the exchange is certain to face a court challenge.

“Federal and District of Columbia law are clear,” read a statement from the American Council of Life Insurers Monday. “The D.C. Health Exchange Authority can only assess carriers of qualified health plans under its jurisdiction.”

Mila Kofman, executive director of the exchange, known as D.C. Health Link, said insurers of all affected policies will benefit from a well-running D.C. exchange — namely, a healthier society that cashes in less often on policies.

But Kofman also acknowledged D.C. simply has no choice: “No other state needs to do this because they have higher population,” Kofman said. “We are in a unique situation.”

Insurers like Unum and Aflac have been among the most vocal opponents of D.C.’s plan. They have argued unsuccessfully to the exchange that their products — which in the event of a loss pay clients directly, and not hospitals or doctors — are more financial planning tools than health insurance options.

Their products are not allowed to be sold on the exchange, so they receive no ancillary benefit, they say. They have also focused on language in the proposed legislation — “all health insurance risks originating in or from the District” — to question if it could someday be used as the exchange’s prerogative to add a tax to life insurance policies and or medical portions of car insurance.

Kofman said that is not the exchange’s intent, and that the tax would hew closely to an established city program that does not tax those additional products.

On Kofman’s side are most of the insurers who compete on D.C. Health Link. If the cost of running the exchange is not spread out across a bigger pool of insurers, they say, the cost of the coverage they offer on the exchange would have to rise significantly, likely making it harder for the poorest to comply with the law.

“One time, we as a city decided to have an arena, the Verizon Center, and whether you like hockey or basketball, all of us got hit with an arena tax,” said David Wilmot, executive director of the D.C. Association of Health Plans. “If an arena was important, and the entire business community was assessed . . . I can think of no more important policy initiative than health care. I don’t see why we can’t make a case for all of us to pay.”

Caroline Pearson, spokeswoman for the market research firm Avalere Health, said the District’s quandary may be the first of many questions about the financial viability of smaller state exchanges.

“Everyone, honestly, has been so focused on getting these up and running that as we move forward in time, we will see the challenge of keeping these financially sustainable,” she said.

Two states have smaller populations than the District — Vermont and Wyoming. Vermont is paying for its exchange in part by raising rates on paid insurance claims. Wyoming is utilizing the federal exchange, which charges insurers 3.5 percent of premiums collected on plans sold on the exchange.

Council member Yvette Alexander (D-Ward 7), chair of the Health Committee, said she was convinced that the exchange had found the right balance in spreading around the pain of paying for the exchange, but said she wanted to make sure the assessment didn’t rise further in the future.

“Overall I think everyone benefits, and overall when you look at this industry, they are making a lot of money — no one is feeling sorry for the insurance industry in the realm that they are hurting for money,” Alexander said.