Hi, welcome to the forum
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To clarify, so there isn't any confusion, there's no such thing as a Tier 4 Spouse visa.
You will be getting a Tier 4 Dependent visa.
A Tier 4 Dependent visa and a Spouse visa are two very different things, so writing both in the same sentence may cause confusion as to which you are actually applying for (a Tier 4 Dependent visa is for family members of Tier 4 visa holders, while a Spouse Visa is for spouses of UK citizens).
As your visa will allow you to work, it shouldn't be any harder for you to get a job than for anyone else in the UK to get a job - the companies are not allowed to discriminate against you simply for being American because you will have the same right to work as any UK citizen.
So it will just depend on each individual company as to what contracts they have available, how long they wish to hire you for and whether you have suitable qualifications for the job.