The research arm of the Department of Justice prepared a study on the likely efficacy of various gun control measures. Their thoughts on baning large capacity magazines (or, as the Times headlined, imposing size limits on bullet cartridges or limiting high capacity ammunition) are interesting:
In order to have an impact, large capacity magazine regulation needs to sharply curtail their availability to include restrictions on importation, manufacture, sale, and possession. An exemption for previously owned magazines would nearly eliminate any impact. The program would need to be coupled with an extensive buyback of existing large capacity magazines. With an exemption the impact of the restrictions would only be felt when the magazines degrade or when they no longer are compatible with guns in circulation. This would take decades to realize.
So unless a final bill excludes a grandfathering exemption and includes a buyback, it will be a Look Good, Feel Good measure unlikely to make any difference. With an effective ban, they conclude their might be an effect on (very rare) mass shootings.
FWIW, my Official Editorial Position has been that banning large capacity magazines is likely to be a political winner whether it makes sense or not. Criminals or aspiring mass shooters (who often display careful planning) will get large capacity magazines if they want them. Or, they may not bother - the Va Tech shooter used ten and fifteen round magazines in two handguns.