You have to be very careful about causation. Does a trade deficient affect growth or does growth affect the trade balance or do third factors affect both?
It is true that when a country's Gross Domestic Product (GDP) is calculated, a trade deficit counts as a negative. But this is a matter of accounting.
By definition, GDP measures the value of the goods and services produced within a country's borders. To tally GDP we take the sum of what households consume, investment by firms and government spending and account for trade by adding what is produced in the nation but consumed abroad (exports) and deducting the value of imports. The (faulty) idea of a “trade deficit drag” comes from this accounting identity – if the difference between exports and imports is large, then a larger number is subtracted from what households, firms and the government consume and the resulting GDP number must be smaller as well.But this does not mean that a trade deficit causes GDP to be smaller.
The flaw in this logic is that both the trade deficit and GDP are outcomes of other, underlying factors. For this reason, there is no simple, straightforward link between the size of the trade deficit and the level of overall economic activity as measured by GDP. Consider a case where the United States has a spurt of growth due to, say, an increase in infrastructure spending. This spending will raise incomes and, therefore, consumption – including consumption of imported goods. This would be a situation where faster growth is associated with an increase in the trade deficit. Alternatively, the trade deficit could very well decline when there is a recession that reduces consumption of all goods, including imports.