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The ads, which will run on Facebook and on search engines, ask supporters to call the individual senators and express support for expanded gun-control measures.

"Too many Americans are dying from gun violence & Congress needs to act. Call Sen. Collins!" reads the ad running against Collins.

The Senate will begin consideration of a comprehensive gun control bill this week or next; it's still unclear whether President Obama will be able to successfully rally support for one of the most politically feasible measures — universal background checks for gun owners.

Opposition from Republicans and some red-state Democrats has resulted in other Obama priorities, including an assault-weapons ban, being stripped from the main bill.

The passage of universal background checks is largely considered the test of whether Obama's push for expanded gun control measures, which followed the Sandy Hook massacre late last year, has been a success.

The president spent Monday in Hartford, Conn., speaking in support of his effort to reduce gun violence. Vice President Biden and Attorney General Eric HolderEric Himpton HolderChristie, Pompeo named co-chairs of GOP redistricting group Democrats look to state courts as redistricting battle heats up On The Trail: Census kicks off a wild redistricting cycle MORE will address the issue on Tuesday at the White House, and first lady Michelle ObamaMichelle LeVaughn Robinson ObamaMichelle Obama looks to mobilize voters for midterms We must mount an all-country response to help our Afghan allies Obamas, Bushes and Clintons joining new effort to help Afghan refugees MORE will advocate for the package at a speech in Chicago later in the week.

The OFA has been working to support his lobbying effort, issuing ads against 16 GOP lawmakers earlier this year. It hopes the online ad campaigns will pressure some of the 11 senators to support the final bill.

While many of the senators targeted in the new ad push reside in red states where any expansion of gun control measures is unlikely to be politically palatable, some — like Collins and Ayotte — are in states that lean blue and might be open to the bill.

Collins is up for reelection in 2014, and a vote for the gun control bill could give her a boost among Democrats and centrists in Maine.

Chambliss, too, represents a possible GOP vote in favor of a bill, as he's retiring in 2014.

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Top aides to the president’s reelection effort relaunched his campaign arm, Obama for America, as the new OFA in January. Now a nonprofit, Organizing for Action can, by law, engage in issue advocacy but not electoral politics. 

It can also receive unlimited donations, and does not have to disclose its donors.

The group has come under fire by campaign finance reform advocates who have expressed concern that special interests can buy “access” to the president through contributions to his advocacy arm, but the group has said it will voluntarily disclose donors.

--This post was updated at 11:33 a.m. on Tuesday.