Obama can't let small groups rule
There is a very good reason President Obama cannot capitulate to Republicans taking the government and national economy hostage to get rid of the ACA. If such a plan, even one so lacking in planning or foresight, were to succeed, then special-interest groups and individuals could obtain the support of some members of Congress each time the budget or debt limit comes up to attack laws they don't like.
They could demand that Roe v. Wade be overturned, prayer be allowed in school, Citizens United (making corporations people) be overturned, clean air and water laws be unfunded. This would give special-interest groups and wealthy individuals even more power and say in our government than they already have.
At the same time, our government would become more dysfunctional and inefficient than it already is without necessarily shrinking, and our economy would be severely weakened on a yearly basis.