In the play "Harvey", Mary Chase does not specify the precise date of the death of Veta Louise Simmons' husband, but we do know that it occurs several years before the date of the play. The death of the husband indeed does serve to increase the anxieties of the women about their social position.
In this period, male and female salaries were still substantially unequal, and there is no indication that either Veta or Myrtle have any significant job skills. They come from a social class where their success is essentially accomplished through marrying rich men. Were Veta's wealthy husband still alive, she would have greater economic security and thus it would be less important for Myrtle to make a "good" marriage. Thus their worry about their reputation stems from the fear that any form of social ostracism will reduce the chances of Myrtle finding a rich man to marry.