Why is it important that the federal gov't maintained budget surplus during the peak phase of the trade cycle?

The why is is easy. The whether is a different question.

If the government doesn't maintain a budget surplus when the economy is good, then the nation debt will never decrease, but continue to increase, year after year. That's called a structural deficit:
http://en.wikipedia.org/wiki/Structural_deficit

Most people find that a horrific thought. The U.S. government total debt now is about $9 trillion.
http://en.wikipedia.org/wiki/National_debt_by_U.S._presidential_terms

With a population of about 300 million, that's about $90,000 per person - man, woman , and child.

A few argue that as long as other countries are willing to lend us the money, there is no need to worry about being in debt.
http://en.wikipedia.org/wiki/Deficit_spending

Of course, they won't (and can't) say how long other countries will be willing to lend if the debt keeps growing.

(Note that government debt - the national deficit - is different from the trade deficit. The trade deficit is financed by people and companies going into debt; the national deficit is financed by the government going into debt.)