I can think of a long list of big problems that the liberty movement cannot fix right now: mass incarceration and the drug war, the police state, income taxes, monetary policy, government debt, war, regulation, transparency and accountability, effective limits on government scope, debt, budget deficits, data security, and IP reform. They all share a strong political component. We must change public opinion before we can do anything about these issues. How do we do that? We can only begin where we are and take a step at a time.
Less obvious but more important problems exist that we can influence right away: peaceful parenting, self-knowledge, DIY skills, mutual aid, etc. (please suggest more in comments.)
We have an immediate effect.
We learn to organize and experiment with different approaches.
We show others what we're about.
We increase the resiliency (antifragility?) of society and show an alternative to government coercion.
When others see us having fun and making a difference, maybe they'll be tempted to join in, first as allies, maybe later as full-on liberty activists.