No, say Chris Erceg, Luca Guerrieri, and Chris Gust, economists at the Federal Reserve Board of Governors. Here is the conclusion from their recent working paper titled "Expansionary Fiscal Shocks and the Trade Deficit."
Our model-based analysis suggests that changes in fiscal policy have fairly small effects on the U.S. trade balance, irrespective of whether the source is a spending increase or tax cut: in our benchmark calibration, a rise in the fiscal deficit of one percentage point of GDP causes the trade balance to deteriorate by less than 0.2 percentage point. Most of the pressure on the external balance due to expansionary fiscal policy is offset by a combination of higher output, and/or a fall in private consumption and investment.
From a policy perspective, our results suggest putting little credence in the idea that fiscal policy changes are likely to exert sizeable effects on the U.S. trade balance. Accordingly, fiscal contraction in the United States is unlikely to be instrumental in narrowing the burgeoning U.S. trade deficit, even if it might be desirable on other grounds.
(Math Alert: The paper is written for economists, meaning it may not be an easy go for the uninitiated.)
UPDATE: pgl comments at Angry Bear (and notes that DeLong and Drezner both commented earlier, a fact I somehow missed.)