An economic analysis on a proposed minimum income model for New Zealand:[0]

  The [basis minimum income] scheme proposed by the Welfare
  Working Group is a significant policy change with large
  economic consequences. The scheme is fiscally very costly
  and would not necessarily achieve its main goal of 
  reducing poverty. The high personal tax rates required to
  fund the scheme are highly distortionary to the labour
  market and to savings and investment decisions, and would 
  be likely to induce a significant behavioural response. 
  This has damaging effects on the tax system and economic 
  growth.

Also of importance, from the same report:

  Although the Gini coefficient improves under all models,
  many beneficiaries (including the disabled, carers and 
  sole parents) currently receive more than $300 per week 
  and would be made financially worse off under a GMI 
  scheme.

At a high level, it seems that the economic reality of providing a basic minimum income to everyone requires a significant increase in taxation revenue. That might be possible with significantly higher GDP per capita, but I'm not certain we're there yet.

[0] http://igps.victoria.ac.nz/WelfareWorkingGroup/Downloads/Wor...

Edit: formatting.