In a country with a parliamentary system, a Prime Minister is chosen by the party with a majority in parliament, or by a coalition of parties if none of them has a majority. The Prime Minister then proposes laws and normally they are enacted by parliament. If parliament rejects an important bill, the Prime Minister has the option to call an election, and let the people decide which they think is right.
Here in the United States, the process is different. In order to become law, the Affordable Care Act has to get a majority of votes in the House of Representatives and 60 out of 100 votes in the U.S. Senate. It then had to be signed by the President and reviewed by the Supreme Court. It seems to me that, whether or not you agree with the law, that ought to be enough.

Hat tip to Buffalo News.
Update: President Obama signed a law providing for continuation of pay of active-duty military personnel.
But now the Republicans in the House of Representatives are threatening to shut down the government unless the Obama administration delays implementation of the health care act. They don’t have the votes to repeal the law, so they are using a blackmail tactic instead.
In my opinion, Obamacare is a flawed plan which is unlikely to work as intended. But it is law, and millions of individuals and thousands of businesses have made plans based on the schedule for implementing it. Shutting down the government would be harmful to the country, but there would be even more harm from the economic uncertainty created by doubts as to whether a law really is law even after it is enacted.
Granted, there are worse things that could happen than a temporary shutdown of government. But it creates unnecessary disruption, unnecessary hardship and also unnecessary expense, because it is more costly to shut down and restart than to continue operations. It is terrible way to run a government.