About 14 million Americans have gained health coverage since Obamacare’s insurance expansion began in 2014 — but those new enrollees haven’t swamped the nation’s doctors’ offices, new research shows.

When the health-care law started, there was concern that an influx of new patients could overwhelm doctors. It’s already hard enough to get an appointment with a primary care provider — wouldn’t millions of newly insured Americans just exacerbate the problem?

New data from 16,000 providers across the country, pulled by the medical records firm AthenaHealth, shows that requests for new appointments just barely edged upward in 2014. The proportion of new patient visits to primary care doctors increased from 22.6 percent in 2013 to 22.9 percent in 2014.

The New York legislature voted down Gov. Andrew Cuomo’s proposal to tax health insurance policies to fund the state’s Obamacare exchange, calling the fees system used by the Obama administration and other states counterintuitive.

The shrinking number of state-run Obamacare exchanges are facing a new problem this year — how to fund their ongoing operations now that start-up grants from the federal government are running out.

In New York, like many other states, Cuomo proposed a tax on health insurance premiums to fund the state-run exchange’s operations. That tactic comes with its own concerns: some states, such as Hawaii, have smaller-than-expected enrollment and the per-policy fees aren’t bringing in enough money.

Rhode Island is considering adopting a tax itself, but due to small enrollment in the tiny state, fees per Obamacare enrollee would likely climb higher than $30 every month, according to Modern Healthcare. Even California, which boasted the highest enrollment of any state in 2014 (but has recently been dethroned by Florida), has had to raise its monthly premium tax.

But according to the New York Post, members of New York’s state legislature refused the extra tax on premiums because the plan would drive up the cost of health insurance for Obamacare customers, defeating the purpose of the exchange and its often-subsidized coverage.

Coping with ever-increasing medical bills is frustrating — and getting more so..

A recent survey by private health insurance exchange EHealth highlights the pressure Americans are feeling. It found that more than 6 in 10 people say they’re more worried about the financial effect of expensive medical emergencies and paying for healthcare than about funding retirement or covering their kids’ education.

People who get health insurance through work and on their own have seen their costs rise dramatically over the last decade.

According to the Commonwealth Fund, a New York think tank, annual increases in work-based health plan premiums rose three times faster than wages from 2003 to 2013. Out-of-pocket costs have also been climbing.

“More people have deductibles than ever before,” says Sara Collins, a Commonwealth Fund vice president. From 2003 to 2013, the size of deductibles has grown nearly 150%.

Whether a person is coping with a severe illness or trying to deal with everyday medical costs, the challenges are many.