(CNN/CBS) — For the second time this year, Americans will be receiving a stimulus check to help ease the strain of the coronavirus pandemic. So when will your check arrive?

A second round of stimulus payments was included in a coronavirus relief package passed by Congress Monday night.

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The deal provides for $600 checks, but experts say it will take at least two weeks for the Treasury to get cash into individuals’ bank accounts after legislation is signed.

“The timing could be more challenging this time, but the IRS could likely begin to get the money out in January,” said Howard Gleckman, a senior fellow at the Urban-Brookings Tax Policy Center.

In March, Congress provided individuals with $1,200 direct payments and couples with $2,400 plus $500 per child under the $2 trillion CARES Act.

As with that first round, the new payments will start phasing out for individuals with adjusted gross incomes of more than $75,000, and those making more than $99,000 won’t receive anything. The income thresholds would be doubled for couples.

It took two weeks after the first bill was passed for the IRS to start distributing the money — but some eligible recipients still haven’t received it, months later.

WHO GETS MONEY FASTEST

The payments do not go all out at once. Those whose bank information is on file with the IRS will likely get the money first because it will be directly deposited into their account. Others will receive paper checks or prepaid debit cards in the mail.

About 90 million people — more than half of those eligible — received their payments within the first three weeks of April after the March deal was signed. Most people had their money within two months.

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Still, about 12 million eligible Americans were at risk of not getting the money at all because the IRS had no way to reach them. While most people received the money automatically, very low-income people who don’t normally file tax returns had to register online before November 21 to provide their address or bank account number.

IRS UNDER PRESSURE

If Congress keeps the eligibility requirements the same as they were for the first round of checks, the process may be nearly as easy as hitting a button. But it could complicate things if the parameters are changed — especially if Congress adds restrictions aside from income.

Additional checks may delay the start of the 2020 tax filing season. A second stimulus check means the agency will have to make changes to the tax return forms, some of which have already been sent to the printers.

December is not an ideal time to add to the IRS’s workload. It’s typically the month when work is done to prepare for the upcoming filing season and more staff may be on leave than usual due to the holidays.

“I believe the IRS will deliver the stimulus checks in a timely manner. It just might be at the expense of the filing season start date,” said Chad Hooper, the executive director of the Professional Managers Association, which advocates for more than 30,000 non-union IRS workers.

“THEY NEED A TON MORE” 

Massachusetts Sen. Ed Markey said that in addition to the stimulus package, president-elect Joe Biden “must make comprehensive economic relief a Day One priority for the new administation.”

“Workers, small businesses, and families may be getting an ounce of relief in this coronavirus package, but they need a ton more. This package must be only the beginning of our work to secure trillions more in aid for the American people. They deserve so much more than this.

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(© Copyright 2020 CBS Broadcasting Inc. All Rights Reserved. CNN’s Katie Lobosco contributed to this report.)