Answer: Strict constructionists: Congress should be allowed to exercise very few implied powers so that government will remain small
Broad constructionists: Congress should be allowed to exercise many implied powers so that government can take a greater role in shaping events
Americans have disagreed about this since the beginning; Jefferson (strict constructionist) vs. Hamilton (broad constructionist) was first major political dispute in US history
Almost immediately following the creation of the Constitution, the Founding Fathers split into two opposing camps over the question of how loosely or strictly to interpret the Necessary and Proper Clause.
One faction, the strict constructionists, was led by Thomas Jefferson. Arguing that "that government is best which governs least," the strict constructionists desired a small federal government, one that would leave most power to the states and to the people. Thus they argued that Congress should only be allowed to exercise those expressed powers specifically listed in the Constitution, recognizing few or any other implied powers as legitimate. Jefferson wanted to ensure that government would charge few or no taxes, mostly leaving the people at liberty to pursue their own objectives free from government interference. Only a very strict reading of the Necessary and Proper Clause, he thought, would prevent the government from giving itself more and more unnecessary power over citizens' lives.
The other faction, the broad constructionists led by Alexander Hamilton, argued for a much more powerful federal government and a much broader reading of the Necessary and Proper Clause. Hamilton, unlike Jefferson, wanted to use the federal government to pursue an aggressive strategy of industrialization and economic development. Hamilton's vision called for the government to organize banks, build roads, and invest in other useful infrastructure, all in the interest of transforming the young United States from a country of farmers into a thriving economic powerhouse. But the Constitution did not expressly grant the government the power to do most of those things; only a liberal interpretation of the Necessary and Proper Clause would allow Hamilton's vision to be considered constitutional. Hamilton and the broad constructionists argued that the national interest could be best served by creating a powerful government able to exercise a wide variety of implied powers, all justified by a loose reading of "necessary and proper."
The argument that began with Jefferson and Hamilton split George Washington's government, leading to the formation of the very first American political parties—Jefferson's Democratic-Republicans opposing Hamilton's Federalists. And the argument has continued, in one form or another, all the way to the present. Should the government be large and strong, able to exercise powerful influence over many areas of American life? Or should it stay small and restrained, leaving the people free to manage their own affairs? Does the Constitution require sharply limited government, or does it allow government to gain broad new powers as needed to deal with new challenges as the world changes?
It all depends on what your definition of "necessary and proper" is.
The strict constructionists have won plenty of victories over the years. Jefferson won the election of 1800 by promising to limit the size and scope of government. The Supreme Court enforced a very narrow reading of the commerce clause from the 1870s through 1937, blocking many federal attempts to regulate economic activity. However, the general trend in American history has been toward the broad constructionist view. In times of war, economic upheaval, and other crises, most people have tended to favor granting the government wide powers of action; over the decades, those gradual expansions of power have led to a government much larger—and an interpretation of the Necessary and Proper Clause much broader—than anything Jefferson or Hamilton could have ever imagined. Almost all of us now accept that the federal government has a huge array of implied powers—powers to impose environmental rules, labor regulations, educational policies, and a hundred other kinds of interventions into American life, even though those powers are explicitly mentioned nowhere in the Constitution. Perhaps our definition of "necessary and proper" will change again in the future, but for now, there seems to be a broad consensus in favor of broad constructionism among most Americans.