I just picked up a used Felt F4X with SRAM Force CX1 components its a single chainring up front with an 11-28t cassette in the rear, I plan on riding this on the road for the time being.
I don’t have any time on this bike yet as I’m waiting on new tires and tubes.

I just moved from a Texas to a state that has a lot of hills, I have not rode in over a year and sucked at what little hills I did encounter in Texas.
My questions is I’m wondering if a 34-36t cassette will help me out with getting up these climbs out here? I know I need to just get some time in the saddle before I start changing components out but I have a feeling these climb are really going to kick my out of shape ass. Any advise would be appreciated or just tell me to stop being fat and ride.

I think you have to determine what derailleur cage you have, as that will limit your cassette biggest cog.

You could also put on a smaller front chainring and net the same gearing change.  Front chainring is about $81.

Good idea! It has a 40t up front, any suggestions?

You moved to a state with a lot of hills?  Like Iowa or Montana?  

I put on a 38t front chainring for a 100 mile 10,000' ride last month and it was PLENTY of gearing.  I wasn't in the right shape for that ride, either.  So.... with your 28t rear derailleur, I'd go 36 or 38.  But you can calculate the gear inches with an on-line calculator and determine the % difference for the chainring that you are looking at.

I would ride the area for a few weeks before I would change anything.
Tons of guys riding 1x11 1x12 bikes around here, several with monster front chainrings.

Knoxville area. Foot hills of the Smokey’s, it’s a lot of hills to me. Like (mouthpiece) said above I’ll probably try to get my lungs back and few solid rides before changing components, but I imagine I’ll end up putting a new chainring on.

I run a wolf tooth 38T front chainring, with a 11-36 rear cassette with a SRAM Rival large cage rear derailleur.  It's close to your standard 2X11 roadie setup.  I live in a very hilly part of Ohio, and an average 30 mile ride yields 2kft of climbing.  I love climbing with my 1X setup, but run out of gear on descents.  

Pros:  Simple, versatile (have 3 front chainrings), and easy to maintain.

Cons:  Keeping pace in group rides is challenging, and spinning out downhill.  

It all depends on how steep the hills are. Spin to win and save your knees.

What is your height and weight?

I am six foot.
Weight goes up and down. 190-200.
I have a 38 in front and a 29 in back. When I am fit and 190 or less I can climb most hills. Usually 7-10 mile climbs averaging 7-8 degrees. I suffer at 10 degrees and up even when I am fit.
Like someone above said, spin, if your cadence slows too much you are not being efficient and probably hurting your knees.

What did you end up doing?

1x on road is dumb. I'd pit a 34 on the front and just ride it while figuring out who to get 2x on there.