No, there is no maximum income limit for a traditional IRA. Anyone can contribute to a traditional IRA. While a Roth IRA has a strict income limit and people with incomes above it can't contribute at all, that rule doesn't apply to a traditional IRA. Yes, you can contribute to an IRA for your unemployed, non-working spouse who files a joint return, but your combined total contribution cannot exceed your combined taxable income or double the annual IRA limit, whichever is less.
Initial tax relief is one of the main things that differentiate the rules of traditional IRAs from Roth IRAs, in which taxes are not allowed to be deducted for contributions. Remember that you are also not subject to income limits when you make contributions to a SIMPLE IRA or an SEP IRA; options that are only available if your employer offers them, if you are a small business owner, or if you are self-employed and can open one on your own. The ability to make non-deductible contributions regardless of income level makes traditional IRAs a valuable retirement savings account that can be converted into a clandestine Roth IRA. You can contribute to a SIMPLE IRA or SEP no matter how high your income is, as long as you meet the eligibility requirements for these types of accounts.
If you don't have taxable compensation but file a joint return with an earning spouse, you can open an IRA in your name and make contributions through a spousal IRA. You may still want to make a non-deductible contribution, either because you prefer to allow your investments to grow tax-free and defer income taxes or because you want to make a clandestine contribution to the Roth IRA by contributing to your traditional IRA and then converting it into a Roth account. People who juggle multiple IRA accounts or who set automatic contributions that are too high could end up investing too much money in a Roth IRA or a traditional IRA.