By Tami Luhby, CNN

(CNN) -- Extra premium subsidies approved as part of the recent stimulus bill will be available on the federal Affordable Care Act exchange starting on Thursday.

Current enrollees and those seeking Obamacare coverage can access the additional help for two years as part of the $1.9 trillion relief package that President Joe Biden signed in early March.

However, those who are out of work likely won't be able to sign up for the $0 premium coverage called for in the stimulus plan until July, according to the Department of Health and Human Services, though they may qualify now for zero- or low-cost policies based on their income. This provision is taking longer to implement because it is new.

The agency is also still looking into whether it can automatically apply the new subsidies to existing enrollees who don't take action. If not, they will receive the enhancement when they file their taxes next spring.

Meanwhile, the 14 states that run their own exchanges have their own timetables for when the larger subsidies will become available.

More help to buy health coverage

The boost in aid is part of Biden's effort to get more Americans covered by health insurance. The relief package makes two changes to the subsidies to address long-standing complaints that Obamacare plans are not affordable for many people, particularly the middle class.

Enrollees will pay no more than 8.5% of their income toward coverage, down from nearly 10%. And lower-income policyholders will receive subsidies that eliminate their premiums completely.

Also, those earning more than 400% of the federal poverty level -- about $51,000 for an individual and $104,800 for a family of four in 2021 -- will become eligible for help for the first time.

The President launched a special enrollment period on February 15 so the uninsured can sign up for coverage. He recently extended the deadline to August 15 to give consumers more time to take advantage of the beefier subsidies.

State-run exchanges, meanwhile, have somewhat different timelines.

In New York, for instance, current enrollees earning below 400% of poverty can access the larger subsides now. They will receive a letter with the new amount in coming days and can log into the marketplace to update their information. If they take no action, they will automatically start receiving the increased aid in June.

But those who made too much to qualify previously and residents who are not currently enrolled have to wait until June to benefit from the heftier help. The Empire State has extended the special enrollment period through the end of the year.

Californians, meanwhile, will start seeing the enhanced subsidies on April 12 and existing enrollees will automatically begin receiving them on May 1. Current consumers will save an average of $119 a month in premiums, according to Covered California, the state exchange, which has also extended sign ups through December.

More people qualify for help now

An additional 3.7 million people now have access to subsidized Obamacare coverage, according to a recent Kaiser Family Foundation analysis. The relief bill broadened availability to 21.8 million people, including both the insured and uninsured.

The average savings for current enrollees will be $70 a month, or 25% of what they pay now, Kaiser found. But it varies widely by income, with those between 400% and 600% of the poverty level saving an average of $213 a month, or 39% of their current premiums. Those earning below 150% of poverty will pay nothing, saving $33 a month, on average.

About half of the remaining 29 million uninsured Americans are now eligible for coverage through Medicaid or a zero-premium Obamacare plan, according to Kaiser. That does not count the jobless, who will also be able to access a no-cost policy.

Many people, however, don't know that financial assistance is available, so it's unclear how many uninsured folks will actually sign up for coverage. Just over 200,000 selected policies during the special enrollment period in the last two weeks of February, before the enhanced subsidies were available.

To raise awareness, the Biden administration is doubling its advertising budget to $100 million and launched a new ad highlighting the availability of no-cost or low-cost plans, thanks to the Democrats' stimulus package. Four out of five consumers will now be able to purchase a plan for $10 or less with the enhanced subsidies, the ad says.

"The Department of Health and Human Services is doubling down on our efforts to ensure consumers, especially those hurting most, are aware that health care coverage is more affordable than ever on healthcare.gov," said HHS Secretary Xavier Becerra.