It is possible, but there are going to be a lot of new codes he will need to know. It will need grounding and bonding, possibly sizing a new feeder, and it is often in a place that is no longer acceptable by code. Physically doing the work is only time consuming, but passing an inspection usually takes extensive knowledge.

Also, disconnecting the service in beyond the capabilities of most amateurs. Also some of the pushmatic panels come in configurations that aren't going to be trivial to just "replace".

Okay, so these comments confirm that this is something my very talented husband shouldn't be doing on his own, but being retired and on a "fixed income", I'm really afraid this is going to take a big chunk out of our savings. Am I correct?

$1'000 - $3,000 depending on where you live. Maybe more.

You may be able to get an electrician to mount the panel and do all the grounding and bonding, etc, and put you on the right track for terminating all the branch circuit wires with the correct breakers yourself (for under $1k). AFCI breakers will be required for most of the circuits. Also, try finding a class at someplace like HomeDepot on the subject.

Replacing the entire electrical panel is beyond the skills of nearly all homeowners. It involves a lot of mechanical skills to get the wiring installed, and you have to understand all the code compliance requirements as you do the work. When you get it inspected the city or county will also expect all work to appear neat and professional (wires run neatly in the box, consistent length of stripped wire for connections, etc.), or its very likely to fail. If it looks anything like a Harry Homeowner project, it won't pass inspection. Its one case where I would definitely plan to hire an electrician.

Bruce