The 360 had extraordinary legs; whether Switch beats it in the US will come down to how much longer Nintendo plan to keep it as their flagship.
It definitely has a shot.

I think the Switch will reach 45mil in the US.

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Switch vs Wii Sales Comparison in Europe - September 2022

This monthly series compares the aligned European sales of the Nintendo Switch and the Nintendo Wii.

The Wii launched in Europe in December 2006, while the Nintendo Switch launched in March 2017. Therefore, the holiday periods for the two consoles do not lineup, which is why there are big increases and decreases.

Switch Vs. Wii Europe:

Gap change in latest month: 227,899 - Switch

Gap change over last 12 months: 2,939,379 - Switch

Total Lead: 2,640,954 - Wii

Switch Total Sales: 28,655,738

Wii Total Sales: 31,296,692

September 2022 is the 67th month that the Nintendo Switch has been available for in Europe. During the latest month, the Switch caught up to the Wii by 227,899 units.

In the last 12 months, the Switch has outsold the Wii by 2.94 million units. The Wii is currently ahead of the Switch by 2.64 million units.

The 67th month for the Nintendo Switch is September 2022 and for the Wii it is June 2012. The Switch has sold 28.66 million units, while the Wii sold 3130 million units during the same timeframe. The Wii sold current Switch sales in month 58.

The Wii sold 33.12 million units in Europe during its lifetime. The Switch needs to sell another 4.46 million units to outsell the Wii in Europe.

Still beating the same old drum despite the Mario Kart 8 Deluxe DLC being confirmed to run through the entirety of 2023. Even a modest holiday quarter 2022 (a flat 3m) will push Switch's LTD sales to 40m by the end of 2022, so the remaining question is as simple as "Can Switch sell another 4m in 2023 and beyond when it achieved 6m in 2022?"

In other words, it would be extremely shocking if Switch couldn't pull this off, even in the unlikely case that the Switch's successor launches in 2023.

EDIT: After seeing Nintendo's financial report that addresses component shortages and a downward revision for shipments, a holiday quarter of 3m in the USA isn't a modest expectation anymore, but rather a slightly optimistic one. It will depend on how Nintendo distributes the stock they will have available.

Regardless, the lifetime target of beating the 360 remains a sure thing.