I am a citizen and resident of Spain who is married to a US citizen. I am trying to travel to the States next week. I have an approved ESTA from one week ago and have already booked my flight. I would like to know what problems I could face and if I am going to be able to enter the US. I am planning on visiting my husband for probably one month. I know I am exempt from the general covid-19-related ban on visiting the US by Spanish residents. my esta got canceled!
The US embassy in Spain has a page that you should read. It says in part:
If you have a valid visa or ESTA and believe, after reading the proclamation and the updated information in the FAQs, that you qualify for an exception, please send an email to MadridNIE@state.gov
Due to the large volume of inquiries, we will only respond to those who have imminent travel and who qualify for an exception. Please note travel for the primary purpose of tourism remains suspended.
A comment to a similar question suggests that if you try to travel without doing this your ESTA will be cancelled. (People are reporting on flyertalk that this is happening.) If that happens, you may be unable to use the VWP in the future.
Also note the last quoted sentence. You may need a more compelling reason to travel than "visiting my husband." You should definitely read the proclamation and give that some thought before writing to the given address.
As the spouse of a US citizen, you are exempt from the bans for people who have been in certain countries in the last 14 days (e.g. the one on the Schengen Area, which you would otherwise be subject to as you are in Spain). So you can enter the US by air if you would normally be able to.
Like any other foreigner entering the US as a visitor, you can still be denied entry due to immigrant intent. This is more so in your case since you are married to a US citizen living in the US, so there is a good chance you want to settle down in the US, and it would be very easy for you to just change your mind and decide to stay, and do Adjustment of Status to get a green card when in the US.