Americans may be in for a cash infusion very soon.

Over the weekend, the Senate passed a sweeping $1.9 trillion coronavirus relief bill that includes boosted unemployment benefits, expanded health insurance subsidies, a more generous Child Tax Credit, and a third round of stimulus checks, this time worth $1,400 apiece.

The Senate bill allows individuals earning up to $75,000 or married couples earning up to $150,000 to collect a full stimulus payment. From there, those checks will phase out, and they'll be cut off completely for individuals earning $80,000 or more and married couples earning $160,000 or more.

All told, around 12 million Americans who were eligible for a stimulus payment during the first two rounds won't be able to collect one this time around. But for those who can still look forward to a stimulus, that money may be coming very soon. In fact, over the weekend, President Biden announced that stimulus payments should start hitting Americans' bank accounts this month as lawmakers rush to get that aid out to those who need it.

Fast-tracked relief

The $1.9 trillion coronavirus relief package that the Senate recently passed still needs to go back to the House for a vote. That should be happening on Tuesday, and no issues are anticipated. Once the bill passes in the House, it will be presented to President Biden for his signature, which is expected before March 14 -- the deadline when enhanced unemployment benefits are set to expire under the last relief bill.

Because the IRS already has a system in place for sending out stimulus payments, the agency can move pretty quickly once it gets the green light. Those who have bank account details on file with the IRS could see their money within days of Biden signing off on a bill. But as was the case with the previous two stimulus rounds, those awaiting a check in the mail may not see their money arrive until April or May, as the IRS can only issue so many checks each week. Furthermore, those who receive a stimulus by mail may not get an actual check -- rather, their funds may come in the form of a debit card that they'll need to activate.

Good news for those in need

While the U.S. jobless rate dropped from 6.3% in January to 6.2% in February, there are still millions of Americans who don't have an income other than the money they collect in unemployment benefits. This next round of stimulus checks will serve as a particular lifeline for people without jobs -- especially those who have been out of work for months on end.

Meanwhile, the tax-filing deadline is coming up in mid-April, and many filers may be due a refund on their 2020 returns. That cash, combined with a stimulus payment, could help a lot of households dig out of their current holes. Furthermore, filers who didn't receive a stimulus payment during the first two rounds but were eligible will be allowed to claim that money on their taxes. So it's possible that some people will receive a total of $3,200 in stimulus money within the coming weeks.

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