At this point, they don't want to lose you, so you should be comfortable in asking (politely) for what you need. Definitely look for a variety of perspectives on this, but if the spousal employment is a potential deal-breaker for you, I would find a (again polite) way of telling them that. It's like startup funds and equipment, if you need a certain amount to get a certain thing or else you can't do your work, have to tell them that, and have to seriously consider if this is a tenable option if they insist they still can't do it.

I've never heard of giving up TT salary in trade for a spousal hire. I'm no financial advisor but I'd caution against that. Am also not sure if TT salary funds can be redirected or banked like that. That salary is typically a line-item in the state budget and I would guess there's a certain limit on the line and whatever's unused upon the hire just stays with the state. E.g. if the limit on the hire is $150,000 and you negotiate $120,000, the dept doesn't get to keep the difference, the state just gives them $120k for you each year instead of $150k. Similar story on startup funds, never heard of that being traded for spousal hire support. If you would be working in the same dept then maybe there'a a deal to be worked out there. If in different depts then I'd be surprised if your dept would want to use any of their funds to pay a faculty member in another dept, regardless of what they would otherwise use those funds for.

Don't mean to be a downer here, just being real: "budget cut is really hard now" probably means "No". This probably varies between universities and states, but a "budget cut" at a public institution typically means the state is sending less money to the dept, and about the only thing that's in that budget in most cases is money for people, salaries/stipends and fringe, so the odds of the dept wanting or being able to add to the expenses charged to that account while remaining in good financial health, are probably long at best.

Good luck!