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I have a dollar that I won't be needing tonight, and I hear that banks are in the market for short-term loans. In fact, the present Fed funds rate is higher than the interest rate on any savings account I can find. Is it possible for me to lend at the Fed funds rate?

You can lend at any rate you like. Finding a borrower is a different matter, as is ensuring that the borrower pays it back.

Few banks will borrow from you at the Fed rate. Currently, rates on savings accounts are less than 0.5% and FFD target is about 2.5%. Plenty of customers still use the savings accounts in spite of this. These customers are your competitors. Why would the bank borrow from you, if someone else will lend for much less?

Another way to think of it is to see the Fed as your competitor. The Fed is an extremely reliable and professional organization. They can borrow from the Fed at the Fed rate. If you lended at the same rate, why would they choose you? What do you offer that the Fed does not? The only thing you can realistically offer is a lower rate.

Looking around, I see some certificates of deposit at 2.5% and even 3%. The former requires at least a 6 mo commitment and the latter is for multiple years. So you can lend money at Fed rate with minimal risk; however, you wouldn't be able to touch the money for many months or years so you probably wouldn't consider it "short term lending".

Buying Treasury Bills is loaning to the U.S. government.

The 4 week Treasury Bill with an issue date of 8/27 got a 2.098% investment rate.

The 13 week Treasury Bill with an issue date of 8/29 got a 1.992% investment rate.

Individuals can buy Treasury Bills, without any fees, through a Treasury Direct account
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If you are asking if you can lend money to the banks, I'm not sure how you would manage that. Maybe it surpasses my level of expertise, but it seems like an overly complicated way to collect ~2.25% interest.

Many online banks are actually beating the Fed Funds rate right now (both Wealthfront and Betterment are over 2.3%). They do this to attract clients that may later opt for investment services that have a management fee.

You can also buy bonds and bond ETFs that would yield similar results.

Wholesale vs retail

For pretty much everything, including loans, the wholesale price is different from the retail price. It is unreasonable to expect the same price when buying a can of Coca Cola as the price you could get when buying a truckload of the exact same cans. It is unreasonable to expect the same price when buying a pound of grain as the price you could get when buying a shipload of grain in the commodity markets. And in the exact same manner it's also unreasonable to expect the same rate for a tiny deposit as for a large one.

The money market deals in large volumes of money. It's not entirely closed, you can participate directly if you want and are able to (many companies and individuals with sizeable amounts of cash do so) - but it's a wholesale market, where the participants expect counterparties who'll ask and fulfil large deals. If you're going to make an offer of $10000, then that's simply not a deal that anybody on that market is interested in; the potential earnings on so tiny deals are not worth the dealers time.

Additional aspect is the 'table stakes' for participating in that market. The market standard communications and settlement channels are prohibitely expensive or otherwise unavailable for a random individual. If you don't have a Bloomberg terminal (single user licence is $20000/year IIRC), then they won't be able to talk to you. If you don't have proper access to interbank real time gross settlement systems, then you can't execute any deal you might agree to.

In short, if you're not trading tens of millions or much, much more, then you're likely not a participant in that market, so you can't get the rate of that wholesale market. An intermediary (retail bank) may take many small deals, consolidate them and put them up in the wholesale market. That's a service that takes some effort, marketing and overhead, and creates a separate retail loan market - with rates that are obviously different from the wholesale loan market.

You can either buy treasuries yourself as the other user told you or invest in a money market ETF that holds treasuries or other short-term bonds for you.

SHY, SCHO, VGSH are all valid ones.

No, for a few reasons. Banks negotiate the rates amongst themselves, it is not determined by the Fed. The Fed's FOMC sets a target for that rate, and the FRBNY OMO desk tries to arrange to meet that target by adding or removing money supply. But it is a target, not a determination. The real rate (called "effective rate", about 2.12% as of last night) is negotiated between pairs of banks, and noone is going to spend the time negotiating with your for an overnight loan of $1.

Also, the loans that have been negotiated get consumated through FedWire. You don't have direct access to FedWire. There is no way for you to get your $1 transferred to the bank and cleared fast enough for it to do them any good.

However, there are banks offering savings accounts that pay more than the FFR. You don't find them on every corner, you have to shop around. You will have better luck doing that than you will convincing someone to admit you to FedWire, and then someone else to negotiate with you for a $1 overnight loan.