With a degree from a British university will it be more difficult to get jobs in the US?
I think it depends where you go and what degree you choose to read. I don’t think there will be much of an issue with a degree from Oxford/Cambridge/LSE, other UK universities are known to be world leaders in their fields, AI at Edinburgh, IR at St Andrews, Art History at the Courtauld Institute, maths/finance at Warwick for example. If you are going on to grad school in the US, stick with the Russell group and equivalents and then it will depend on grade of degree and GRE, MCAT etc.
agreeing with @elguapo1, and adding that as with most undergraduate degrees, what you doing during your time in college will matter a lot- research in a relevant area, work experience in your field during the holidays, etc.