Minimum wage workers are only employed by certain companies, so you would not see a direct one to one increase in prices along with the minimum wage. Something like fast food would be more greatly impacted, but that really isn't an essential part of anyone's budget. Stuff like rent and utilities wouldn't really be effected, and that is a huge part of the average budget.
Now, this isn't to say that a higher minimum is always better. We would have to find a sweet spot that balances the benefits to low wage workers against increased prices.
When minimum wage goes up what do you think happens to the guy's wage who is earning 10 cents above minimum wage?