Two things -
1) The current battle is not about Obamacare. It is about who controls the purse. The Constitution gives that power to Congress. They can exercise it anyway they like., One big spending bill is allowed. Several small bills (like to pay CDC workers) are also allowed. The president may want a so-called clean bill giving him everything he wants. It's not his call.
A parent may give all a child's allowance in one package, or give specific amounts for specific purposes. It kind of depends on how responsible the child is. So far the big spender in the White House has not proven himself to be responsible.
2) The country will not default. If your credit card company refuses to up your credit limit, that does not automatically cause you to not pay your mortgage. It does mean you will have to cut back on discretionary spending. No raises for federal workers, no clean energy grants, no foreign air, etc, etc.