The first step for a state that wants to secede is to kick the National Guard out of their state, and replace it with a true state militia.
I guess the states were too cheap to fund their own militias so they passed their responsibilities onto the feds.
Now any time the feds want to start a war anywhere and run out of armed forces personnel they can start drawing from the National Guard.
But if a state had its own militia it could tell the feds to pound sand. Their militia would be too busy guarding their borders, supporting local authorities in times of extreme duress (e.g. hurricanes, forest fires, etc.) and protecting the citizens of the state.
As long as the National Guard continues to do the job that state militias were meant to do, there is no hope/fear of secession.
You're sadly correct about state support. Almost no one knows what portion of their state's budget goes to their state military department. I believe most would be shocked. A few years back Georgia had a line item of less than $1.5M for the State DoD. The feds foot virtually all the bill for the National Guard.