Which Intex? Hard frame or EasySet Donut?

The biggest problems I see are:
First, as mentioned, if the filter is too small for the pump (or the pump is too big for the filter--same thing). In that case you may be able to get a reduced-flow impeller for the pump, which would be the cheapest solution--You got a BIG margin on a $5 pump&filter!

The second problem is that most filters are 1.5" plumbed, and most Intex pools are 1.25" fitted--and you cannot increase the size. This mean that you'll need to step-down in fittings to 1.25" at some point, which will increase pressure and may damage the pool at that point. ANOTHER good reason for the reduced-flow impeller...

But once you have that solved, hook up a solar panel and you'll have a HUGE hot tub, complete with jet!