Swallowing is a complex function. When our anatomy is changed abrupbtly by surgery, radiation, scarring and swelling we can expect trouble swallowing. Expect it but know that there is something you can and should do about it especially at this early stage in your husbands recovery.
Get a referral to a speech therapist/pathologist, and he/she will likely want to do a Modified Barium Swallow study. It's a painless x-ray that allows us to view the entire swallow process and identify what the problem is and how to solve it.

I have a huge amount of empathy for those who rely on a G-tube because of severe swallow problems. For some - that is an inevitable and harsh outcome. The thing is though, we don't know that for many months to years after the problem presents itself. The vast majority of head and neck cancer Patients, can improve their chances of a better outcome (no choking, no G-tube long term) IF they have good assessment and treatment of their swallowing problem -the sooner the better. So many on this site need speech therapy treatment to improve their swallowing problems - the problem is that most doctors don't recognize this and the Pt is put in the position to push for it - I can't encourage you enough to PUSH for assessment and treatment. If your leg were paralyzed you would not just wait for it to get better, you wouldn't just go see a doctor or physical therapist once a month to see if it's any better yet - you would have active and regular treatment to get better - and that's what those with swallowing problems should do.
Don't wait - get a referral - the swallow is too important to just take the "wait and see" approach of too many physicians.