By Katie Lobosco, CNN

(CNN) -- Congress has authorized nearly $4 trillion in spending over the past year to help address the economic crisis caused by the coronavirus pandemic, but only about $3 trillion of it has been spent.

Roughly a third of that money went directly to struggling families through stimulus checks, expanded unemployment payments and food stamps. That leaves about $1 trillion that hasn't been disbursed yet, even as President Joe Biden is calling on Congress to approve another $1.9 trillion Covid-19 relief package.

Administration officials say the risk of doing too little is far greater than the risk of going too big, while many Republican lawmakers -- and at least one well-known Democratic economist, Larry Summers -- are concerned about the price tag of Biden's plan. A group of 10 GOP senators have proposed a $618 billion package, which would narrow the number of people eligible for stimulus payments and provide less school funding than the Biden plan.

Much of the $1 trillion previously authorized but as-yet unspent funds are scheduled to be used over time, and only a small portion will never be spent, according to the Committee for a Responsible Federal Budget, a fiscal watchdog group tracking the spending.

Here's what hasn't yet gone out the door:

About $500 billion left from March 2020

Congress passed three major stimulus packages last March and April. At $2.7 trillion, the CARES Act was the largest and put in place some of the key benefit relief programs that Biden is working to extend, joined by lawmakers from both parties.

About 80% of the money from these prior bills has been disbursed. About half of what's left is related to ongoing Medicaid spending and some long-term small business loans, known as Economic Injury Disaster Loans. The Medicaid matching payments to states will continue as long as there is a public health emergency. The disaster loans remain available to small businesses. Though they carry low interest, they weren't as popular as the Paycheck Protection Program loans, which are forgiven if used on qualifying expenses.

It's possible that some of the relief programs, like the the 13-week extension of unemployment benefits in the CARES Act, may end up costing less than expected, according to the Committee for a Responsible Federal Budget.

School funds disbursed but not spent

The amount of money the federal government should give to school districts to help them reopen buildings safely has emerged as one of the big differences between the Biden and Republican proposals for additional stimulus spending.

The White House is calling for $130 billion while the plan from 10 Republican senators proposed $20 billion, citing concerns that a big chunk of the money authorized in earlier packages remains unspent.

While the $68 billion authorized in December has been disbursed by the federal government, just $4.4 billion of that pot had been actually spent by school districts as of last month. Administration officials say that money will likely be spent in the coming weeks and argue that the funding in Biden's plan would help avoid layoffs into the next school year, as well as help with reopening.

Half of the money left was in the most recent stimulus

Roughly half of the unspent money comes from the package approved by Congress in late December, when lawmakers passed a $915 billion relief bill that provided $600 stimulus payments, extended unemployment benefits, reopened the small business loan program and various other spending.

Some of this money is intended to last for months. For example, the Committee for a Responsible Budget estimates that another $120 billion will be spent on boosted federal unemployment and food stamps before the end of the year. The unemployment benefits are set to expire in March and a 15% increase to SNAP benefits that will continue for six months.

More than $200 billion remains for the Paycheck Protection Program, which recently reopened to small businesses for a second round of loans and is available through March. The money is going out quickly. More than 891,000 loan applications totaling $72 billion were approved by the Small Business Administration in the first few weeks.

The vast majority of the $166 billion allocated for the direct $600 per person payments has been delivered by the Internal Revenue Service, which began sending out the money in late December. There's about $35 billion remaining, which could likely be claimed when eligible people who didn't receive their money file their 2020 tax returns.