It can’t hurt. And who knows? Just possibly it may help.
Six Senators, including two Republicans, have introduced a new proposal to curb illegal gun trafficking.
The law would stiffen penalties for buying or selling a weapon to a “straw purchaser” on behalf of a person otherwise prohibited from buying weapons. The law would define straw purchasing as a federal crime and also impose new restrictions on the export of U.S. guns to other countries.
To appreciate the law, you have to appreciate the incredible laxity of current rules on bogus gun sales.

From the Jefferson County, Colorado, sheriff department's investigation of the Columbine massacre:
The investigation revealed that a friend, Robyn Anderson, accompanied Harris and Klebold to a gun show in late 1998 since she was of legal age to buy a firearm. At the gun show, 18-year-old Anderson purchased two shotguns and one rifle for the two killers. Those same guns were later used in the Columbine killings.
Anderson denies any prior knowledge of their plans. No law, state or federal, prohibits the purchase of a long gun (rifle) from a private individual (non-licensed dealer). Because of this, Anderson could not be charged with any crime. If Anderson had purchased the guns from a federally licensed dealer, it would have been considered a “straw purchase” and considered illegal under federal law to make the purchase for Harris and Klebold.
Now to the limits of the proposals from Sens. Richard Blumenthal (D., CT), Susan Collins (R., ME), Richard Durbin (D., IL) Kristin Gillibrand (D., NY), Pat Leahy (D., VT), and Mark Kirk (R., IL).
It will remain legal for individuals to buy very large numbers of guns and to buy them very often. The law enforcement resources for ensuring that such guns are not distributed to unlawful persons will remain very constrained. Not only has the office of the director of the Bureau of Alcohol, Tobacco, and Firearms been left empty for—hold your breath—six years, but Congress has also voted down the basic elements of any kind of gun law enforcement scheme.
From the New York Times:
[W]hile detectives on television tap a serial number into a computer and instantly identify the buyer of a firearm, the reality could not be more different.
When law enforcement officers recover a gun and serial number, workers at the bureau’s National Tracing Center here—a windowless warehouse-style building on a narrow road outside town—begin making their way through a series of phone calls, asking first the manufacturer, then the wholesaler and finally the dealer to search their files to identify the buyer of the firearm.
About a third of the time, the process involves digging through records sent in by companies that have closed, in many cases searching by hand through cardboard boxes filled with computer printouts, hand-scrawled index cards or even water-stained sheets of paper.
So the straw purchase bill may not amount to much. It may not pass the Senate, and even if it does, it will run into trouble in the Republican-controlled House. Still—baby steps.