The NRA has a long track record in electoral politics, and is viewed by lawmakers in both political parties as unusually effective. Bloomberg's organization has yet to be tested.
In the AP-GfK poll, among independents, support for stricter gun laws dipped from 60 percent in January to 40 percent now. About three-fourths of Democrats supported them then and now, while backing among Republicans for looser laws about doubled to 19 percent.
The survey was conducted from April 11-15 by GfK Roper Public Affairs and Corporate Communications. It involved landline and cellphone interviews with 1,004 randomly chosen adults and had a margin of sampling error of plus or minus 3.9 percentage points.
Associated Press writer Laurie Kellman, AP Director of Polling Jennifer Agiesta and news survey specialist Dennis Junius contributed to this story.
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