Remembering that my employer had to do all the paperwork right on day 1, my guess will be that they probably would prefer your wife to have her working rights before starting. Especially in this climate with many Spaniards out of work, they´d be a little be more cautious, moreover, most of them take advantages of government incentives (such as, if your wife is young and can work on an internship contract they get grants from government, etc).. so it really depends on the situation and type of job.
Plus working will also mean paying Social Security, so without proper permit and Social Security number (which she´ll need to show the proper NIE de Cuidadanos in order to get), this could be a bit tricky for employers.
Of course everything depends… if she works in the black, that´ll be easier.
With this working climate, she´ll probably need all the time whilst paperwork is being processed to find a job anyways!! Apparently it takes an average 6 months to find a corporate job here, and for an experienced hire.
Otherwise, why not bum around til the card/paper (guess new format is now a piece of paper) arrives! Mine took 2ish months.