Unions, representing their employees, negotiate with the employer for the benefit of the employees. When big business refuses to negotiate, the employees go on strike to get the employer back to the negotiating table.
In government, the Republicans (union for a minority of U.S. citizens) are trying to negotiate a contract (budget) with the Democrats (big business) but the Democrats refuse to negotiate and the president would rather dictate than negotiate. Thus, the result is a strike (government shutdown).
The majority want a balanced budget and a plan to pay down the debt. Why won't the Democrats and the president negotiate such plan? The Affordable Care Act (Obamacare) benefits those who do not have insurance at the expense of all others. But this is not the main issue in balancing the budget. Congress has had five years to produce a full year's budget and has yet to do so.
Just as unions are not solely to blame for a strike, neither the Republicans nor the Democrats are solely to blame for the government shutdown. In fact, they are all to blame equally with President Obama.