What would happen in the US if Asian imports were cut off?

Worse than you think. While Intel CPUs are mostly made in the US still, a while ago at least they were packaged in Asia. Everything for the CPUs I work on now is done in Taiwan. State of the art parts are designed to the process for a specific fab. It would not be very fast or easy to move production from TSMC to Intel.
Most contract manufacturers are in Asia also. So, even if you had the parts you wouldn’t be able to assemble them.

I suspect it would be like WW II but worse, with the military taking over what production is left and the civilian market basically drying up to near zero.
We’d have food and oil, at least.

Just look at the flooding in Thailand, which produced a large number of hard drives.

It took awhile for the hard drive market to come back.

Another thing to look at it, historically when a market is dried up, the answer often leads to a better solution.

Like when cotton was cut off from Great Britain, it responded by finding other areas of the world to grow cotton and import from.

If the crazy dictator was in China, the answer might be “yes”. But again, that would bring disaster on China and environs too.

I think we have the technology to rebuild if necessary - but the disruption would be wide and erratic. There are so many things we don’t make, and some things like chips where we make some quantities, but nowhere near enough. I agree we would probably see a long period of deprivation and rationing, a time when the government would walk in and tell certain companies what their priority in fabrication would be in order to kickstart the manufacturing sector.

For example - we (probably?) don’t make flatscreens, certainly not in the quantities needed; nor dozens of other critical computer components. That would mean as certain elements of IT infrastructure failed, companies would improvise or get by without. Productivity suffers for example because there are not enough computers to go around. Perhaps a short-term industry would grow up over repairs; after all, we don’t repair many modern devices because the manpower-vs-replacement-cost makes it uneconomical. Make replacement expensive enough and people will repair. Also, there’s hidden inventory. I have 5 flat-screens of various age and quality at home. If suddenly those had high resale value, I might part with them. (4 more if you count laptops of various ages, plus my wife and I have 3 iPads and 4 iPhones).

Even if we could get past the initial stage, though, we would then adjust to a hemisphere where things had a value related to the cost of manufacture, rather than items made by someone paid a dollar a day. What happens then when the other side of the world resumes trade is another interesting speculation.

But the American economy would also suffer as a result of decreased demand for American goods and services. Most people have so far focused on imports from Asia. Truth is that the US and Asian countries are trade partners, and the US exports to Asia make up a significant portion of American trade:

http://www.ustr.gov/about-us/press-office/fact-sheets/2012/june/us-tpp-increasing-american-exports-supporting-american-jobs

This is a bit of a tangent, but a lot of people have mentioned that we (US) no longer know how to make stuff. When things were mechanical, someone with engineering talent could look at it and see how it worked, so it wasn’t that hard to copy.

With so many things today being based on nanometer-scale electronics, is it even possible to reverse engineer things anymore? Would we literally have to go back to 1970’s technology, as one response claimed? Do we at least have access to technical manuals that would tell us how to do stuff, even if we don’t presently have the machines to do it, so we wouldn’t have to completely reinvent everything?

It’s a total BS claim.
The US manufactures products over the entire spectrum - from handmade to the most sophisticated computer chips. For example, intel’s Core series of processors is made in the US, and some of them have billions of transistors on the die.

And, there is still steelmaking in the US, although it tends to be specialty steels.