。
I might just give up right away and take a nap.
Literal
Immediately give-up-[and-て] nap [object-を] do [might-かも知れない].
Two key structures: the te-form 諦めて connects the two actions sequentially ('give up and then nap'), and ~かもしれない expresses possibility or uncertainty ('might'). 昼寝 literally is 'noon-sleep,' the standard word for a nap or siesta. The plain form is appropriate for self-talk or casual speech.