Republican Sens. Jeff FlakeJeff FlakeReid bids farewell to the Senate Reid defends relationship with McConnell in farewell speech Graham, Durbin 'encouraged' by Trump's comments on Dreamers MORE (Ariz.), Saxby ChamblissSaxby ChamblissWyden hammers CIA chief over Senate spying Cruz is a liability Inside Paul Ryan’s brain trust MORE (Ga.), Johnny IsaksonJohnny IsaksonGOP senators wary of nuking filibuster SENATE: Republicans defy odds to keep majority A banner year for U.S. leadership on aid effectiveness MORE (Ga.), Dan CoatsDan CoatsTrump's Cabinet: What jobs are left to fill Trump narrows secretary of State field to four finalists 2016’s battle for the Senate: A shifting map MORE (Ind.), Chuck GrassleyChuck GrassleyMnuchin, Price meet with GOP senators Business groups express support for Branstad nomination 10 no-brainer ways to cut healthcare costs without hurting quality MORE (Iowa), Susan CollinsSusan CollinsDems, greens gear up for fight against Trump EPA pick Medicare looms over Trump-Ryan alliance Senators crafting bill to limit deportations under Trump MORE (Maine), Dean HellerDean HellerReid bids farewell to the Senate Reid defends relationship with McConnell in farewell speech Governments and businesses: Teaming up for taxpayers MORE (Nev.), Kelly AyotteKelly AyotteDem senator tears up in farewell speech Juan Williams: McConnell won big by blocking Obama Battle brews over Trump’s foreign policy MORE (N.H.), Rob PortmanRob PortmanSenators to Trump: Get tough on Russia over Ukraine John Glenn dies at 95 John Glenn hospitalized MORE (Ohio) and Ted CruzTed CruzThe Hill's 12:30 Report Cruz defends Trump's Taiwan call Ark., Texas senators put cheese dip vs. queso to the test MORE (Texas), as well as Democratic Sen. Martin HeinrichMartin HeinrichBudowsky: Did Putin elect Trump? This Week in Cybersecurity: Dems press for information on Russian hacks Overnight Cybersecurity: Last-ditch effort to stop expanded hacking powers fails MORE (N.M.), are being targeted in the effort.

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 H. HolderTop Dem signals likely opposition to Sessions nomination Instead of 'hope and change' Obama gave progressives Trump Republicans want to grease tracks for Trump MORE will address the issue on Tuesday at the White House, and first lady Michelle ObamaMichelle ObamaThe Hill's 12:30 Report Depleted Dems look to Senate for 2020 nominee Would it be legal for Trump to give his son-in-law a White House gig? 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.

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.