Legally, they cannot just nab you. The usual (?) option is that authorities in the US request extradition pursuant to the US-Mexico extradition treaty via the Department of Justice, and if the paperwork is in order, this can result in a Provisional Arrest Warrant (and arrest) in Mexico, which will be carried out by the Mexican federal police. This is true whether or not you go to the US consulate. After a hearing in the Mexican courts you might be extradited (or not, but DoJ presumably doesn't proceed with cases that they will lose). Extradition is not possible for every offense, so you would have to look at the offenses listed in the treaty, and whatever the Arizona warrant is about. You can't be extradited for parking tickets, you can be extradited for murder: whatever it is, it has to be a crime in both places, and has to be subject to a minimum one year imprisonment. Also, if you are a Mexican citizen as well, you cannot be extradited unless the Mexican authorities agree to (whereas there is no choice if you are only a US citizen). An alternative is deportation, which would overcome limitations related to extradition, but it's not clear what the requirements for deportation from Mexico are (typically illegal presence, unclear whether Mexican authorities can or would try an end-run around official extradition procedure).
Although consulates enjoy a degree of immunity from local law, a consulate in Mexico is still Mexican territory, subject to Mexican law. If you are in the consulate, Mexican authorities cannot enter without permission to arrest you. They also cannot arrest you without a warrant (see Art. 16 of the Mexican constitution). Consular staff also cannot arrest you (if you are not caught flagrante delicto). Nor are they authorized to execute a US warrant in Mexico (thus they have to go through the process of judicial review to send you back to the US, and why a Mexican warrant is required). See this Q&A, relevant to the status of embassies: what is relevant to us is that both the US and Mexico operate under the rule of law, so the issues surrounding Syrian refugees in the Syrian embassy do not arise here.