Come next week, hundreds of thousands of people will be watching that show.
Literal
Next-week [become-になる-when-と], several-tens-of-thousands [even-も] [possessive-の] people [subject-が] that program [object-を] watching-is [probably-だろう].
何十万人も packs several markers: 何 ('what/how many,' here as an indefinite 'many'), 十 ('ten'), 万 ('ten thousand'), 人 ('people counter'), and も ('as much as'). 何十万 = 'hundreds of thousands.' The も emphasizes the large quantity — 'as many as.' ~ているだろう = ongoing state + probability.