Is legislating minimum wage a prudent economic decision for combating poverty?

Raising the minimum wage sounds on the surface like a wonderful thing
for poor people in America.  However, it would come with many costs.

It would immediately lead to increased prices at McDonalds and WalMart
and many other establishments who rely heavily on lower paid workers. 
Inflation would be extremely difficult to control during the
transition period.

Another unfortunate side effect would be that in the long run,
McDonalds and WalMart (along with many many other companies) would
find more and more ways to automate their services to become less
reliant on labor.  Supermarkets would have many more self checkout
lines and fire many checkout servers.  We'll be placing our McDonalds
orders on a touch screen and simply inserting cash/cards to pay. 
Customer service calls would almost never reach a real person but
instead we'll be talking more and more to machines.  Perhaps cleaning
innovations will become the trend where toilets, sinks, even floors
can clean themselves and not rely on janitors.
Any economist will tell you that the rising cost of low level
employees will lower the demand for low level employees and therefor
create more unemployment among them.  The lucky ones will raise their
standard of living, while the rest will go from poor to completely
broke as their previously bad job turns into no job at all.

Many people would argue with me, but it seems obvious that the costs
outweigh the benefits when it comes to raising the minimum wage.

First of all, raising the minimum wage is really a political topic
more than a pure economic one.  With that in mind, one must define
poverty before discovering whether a minimum wage will fight it. 
Since the poverty line is a political question, I offer no advice on
where poverty should begin.

A minimum wage is really a price floor that holds wages at a given
amount.  This only has an effect on the market if the floor is set
above the market wage rate.  In the event that it is below the market
rate, then there is absolutely no effect on the market.  When a floor
is above the market rate, the labor demand does not change. However,
the quantity of labor demanded at the floor wage will ultimately be
less than the quantity of labor demanded at the market wage. 
Increasing the wage rate will increase unemployment, because the
number of people that would work for a lower wage now cannot due to
the minimum.  The number of newly unemployed equals the difference
between the quantity of labor demanded at the market wage and the
quantity of labor demanded at the minimum wage.

Furthermore, the increases in wages have repercussions in the input
costs of firms.  If, all other things equal, a firms wages go up, then
seventy percent of their costs have risen.  Because wages are a
substantial majority of firm costs, a significant increase in the
minimum wage could cause firms to become unprofitable or create cost
push inflation, forcing firms to raise their prices at every level of
output to try to stay profitable.  Strong competition from overseas
would likely cause many problems for firms trying to make money by
raising prices.  Firms would likely overhaul their production lines to
try to cut costs that were still in their control.

In reality, the average hourly wage is about $16.00 in the US far more
than the minimum wage of $5.50.  Modest increases in this amount would
not spread havoc among most firms who pay more for labor anyway.  The
only firms that would see changes would be those whose employees are
paid the minimum with no potential for raises.

If the country was growing very rapidly at the time the change was
implemented, meaning all firms profitability would not be materially
affected, then it could accelerate the growth if the wage earners save
the money, increasing the amount of loanable funds, lowering interest
rates, increasing investment spending, increasing the capital stock,
increasing marginal product of labor and productivity of labor which
could lead to a natural increase in wages due to the new value of
labor.

I studied this:  Here are my results:
The results show that over a one-to-two year period, minimum wages
increase both the probability that poor families escape poverty and
the probability that previously non-poor families fall into poverty.
The estimated increase in the number of non-poor families that fall
into poverty is larger than the estimated increase in the number of
poor families that escape poverty, though this difference is not
statistically significant. We also find that minimum wages tend to
boost the incomes of poor families that remain below the poverty line.
The evidence indicates that in the wake of minimum wage increases,
some families gain and others lose. On net, the various tradeoffs
created by minimum wage increases more closely resemble income
redistribution among low-income families than income redistribution
from high- to low-income families. Given these findings it is
difficult to make a distributional or equity argument for minimum
wages.