To have an independent right of residence for more than three months under EU freedom of movement rules, your wife is indeed required to either work, study or have sufficient resources. Sufficient resources means an income high enough not to “become a burden on the social assistance system of the host Member State” and health insurance.
In particular, being above the threshold for basic welfare benefits is enough (to give you an idea, in countries like France or Germany, we are talking about an amount on the order of ~€500 a month per person, well under the minimum salary required to qualify for a blue card, which is more like €3000 or €4000 a month depending on the country and profession). Savings could work too, if they are accessible.
Now, if she would have to sponsor your residence permit, she would almost certainly be asked to show that she qualifies. But it seems you will have a residence permit of your own and are only worried about her status so things are a little different. What the rules say is that she does not have a right to stay and can be challenged and asked to leave. That does not mean that each and every EU citizen has to show they qualify and obtain a residence permit or leave immediately, lest they are illegally present in the country.
Unlike Brazilian and other third-country nationals, EU citizens do not generally need to secure a residence permit in advance and would certainly not face deportation even if they fail to complete some formalities in time. Procedure-wise, it works the other way around. So until you are challenged to prove that you qualify, you're fine to stay. But if you are asked to leave, then you cannot invoke your freedom of movement rights if you don't qualify in one of the ways listed at the beginning.
The formalities differ a bit but in practice, in many countries, you can therefore simply stay without doing anything special, as long as you don't attract attention to your situation. It's only if you need to sponsor a spouse, apply for welfare benefits or become undesirable in some way that your lack of a sound claim to residence under freedom of movement rules becomes relevant.
That's definitely the case in France or the UK for example, and more-or-less in Germany, the Netherlands or Belgium (except that in those countries everybody has to register their address with the authorities or risk a large fine, but that's unrelated to your status as an alien). You can check the europa.eu to see if there are additional formalities in the country you are planning to settle in.
Also, if you are married and sharing an household, there is no reason that your income/wage would not count as sufficient resources for your wife to stay as an economically non-active EU citizen. Once again, if she needed to sponsor your residence permit you would have a bit of a chicken-and-egg problem and it's not clear that she would qualify because you cannot prove you have an income before getting your work permit. But if you get your permit on your own, once you work and have an income, all that is moot. If needed, she could then prove that you have sufficient resources and hopefully she will get health insurance through your work as well (here again, it depends a bit on the specific country, the systems differ).
Finally, note that your status in the country might have some legal consequences down the line. If you stay for a few months in Sweden under freedom of movement rules, you could use the “Surinder Singh route“ to move back to Portugal under the same rules (see An EEA returning to original country does "EU law" or "Domestic law" for Family Reunification). You would also get a residence card as “family member of an EU citizen” which would grant you visa-free entrance to the UK under some conditions (not very relevant for Brazilian citizens but useful for others). And after five years you would become a permanent resident with very strong rights to stay in the country even if your situation changes. None of this is true to the same extent for blue card holders.
