Minimum wage vs wage subsdies Many politicians argue that the minimum wage is essential for providing an sufficient standard of living to all. However, there are many issues binding price floors predicted by standard supply and demand theory. Why couldn't wage subsidies be used instead? I know that they are used. However, why do politicians always argue for increasing the minimum wage as opposed to increasing wage subsidies?

what advantages does the minimum wage have versus wage subsidies?
We could distinguish between two kinds of "wage subsidies": 

A) The government pays to the firm part of the wage cost, usually social security fees.

B) The government pays to the employee a markup on his wage. 

In scenario A, labor supply is not affected but labor demand shifts outwards: the tendency should be higher employment and higher equilibrium wage (so eventually more disposable income for the workers). Usually, what is observed is that employment rises (after all, usually such programs are on  condition of net new jobs creation in a company), but wages do not increase (i.e. firms don't share the subsidy with the employees). So no betterment of standard of living of those employed.

In scenario B, take-home income will increase at no cost to the firms. So now, workers know that if the current wage is $w$, if they work they will receive $w+s$. This will shift the labor supply curve outwards (because now it responds to $w+s$), while the labor demand curve will remain unchanged (which still responds to $w$ only). This will tend to result in higher employment and lower equilibrium wage. But this contradicts (and partly or wholly offsets) the very purpose of the measure, which is not to increase employment, but to increase disposable worker income.  

So in both cases, wage subsidies are more about employment rather than income, while minimum wage is clearly about income and standard of living of those employed, even though it may hurt employment.

...and one cannot avoid in these matters a dash of political economy and political science (as well as social psychology): subsidies bear always a risk of fraud, and are always suspect of being an instance of pork-barrel politics. Moreover, they are mostly seen as measures in time of macroeconomic (or regional) recession/depression, where the main concern is to boost employment.  

On the other hand, minimum wage is not about a faltering economy as regards activity and level of production/income, but about market failure as regards distribution of income. Issues of distribution are inextricably linked to issues of fairness, and this creates a more passionate political agenda, occasionally  satisfying also the expectations of the public for a "strong government" which, "when markets create unjust misery", intervenes "decisively", imposing by decree "what's fair" (or fairer).