A Boutique Immigration Law Firm Serving the Bay Area

Can a spouse of a US citizen living abroad obtain a work visa based on the marriage only?

No unfortunately not. If you are coming here to work, then you would need your employer to sponsor you for a work visa. Depending on the type of work you will be doing, there might be other visas you can use to enter. But, simply being married to a U.S. Citizen with no green card, employment authorization document, etc. will not allow you to work here.