What key part of the New Jersey plan is not in the Constitution today?

The New Jersey Plan proposed the establishment of what's called a unicameral legislature. This is a legislature which consists of one chamber, instead of two (e.g., the United States Senate and the House of Representatives). The thinking behind unicameralism is that it is more representative of majority opinion than a bicameral system, and this was certainly one of the considerations in the minds of those proposing the New Jersey Plan. To that end, it was explicitly designed to be a more democratic system, one that would give expression to the democratic principles contained in the Declaration of Independence.
Opponents of the New Jersey Plan, however, were worried that it would lead to mob rule. Without a second chamber to check its power, an elected chamber would, they feared, ride roughshod over the rights of the minority, shamelessly pandering to public opinion instead of doing what was right.
Many of those opposed to the Plan were unashamed elitists who believed that the democratic temper of the people should be kept in check by the wisdom and prudence of men of property, such as themselves. This attitude would find constitutional expression in the establishment of the United States Senate, which wouldn't be directly elected by the people until the ratification of the Seventeenth Amendment to the Constitution in 1913.

At the Constitutional Convention, there was a great deal of debate about the legislative branch. There were some states that wanted representation in Congress to be based on the population of the state. This was part of the Virginia Plan, which called for two houses of Congress. This plan would give larger states more representatives than the small states, as representation would be based on the population of a state. This plan worried the small states. The people in the small states were fearful that their concerns would not be heard or addressed.
The small states developed a different plan called the New Jersey Plan. In this plan, there would be a one-house legislature and representation would be equal for all states. Eventually, a compromise was reached. It called for two houses of Congress with unequal representation in one house and equal representation in the other house. Thus, the part of the New Jersey Plan that was not included in the Constitution was the part about having only one house of Congress.