The answer lies in the words of James Madison, America's fourth President, and the man often referred to as "The Father of the Constitution." Here's what he had to say about the House of Representatives and funding (Some emphasis is mine):
"The House of Representatives can not only refuse, but they alone can propose the supplies requisite for the support of Government. They, in a word, hold the purse; that powerful instrument by which we behold, in the history of the British Constitution, an infant and humble representation of the People gradually enlarging the sphere of its activity and importance, and finally reducing, as far as it seems to have wished, all the overgrown prerogatives of the other branches of the Government.As the closest representatives of the people (the majority of whom oppose Obamacare) it is the House's duty to use the power of the purse to fulfill the people's wishes. Refusing funding, reducing the prerogatives ("excesses") of other branches of government, and redressing ("remedying") the grievances of the people are right in line with what the Founders had in mind when they wrote the Constitution.
"This power over the purse may, in fact, be regarded as the most complete and effectual weapon, with which any Constitution can arm the immediate Representatives of the People, for obtaining a redress of every grievance, and for carrying into effect every just and salutary measure." - James Madison, Federalist Papers #58 (1788)