Republican Sens. Jeff FlakeJeffrey (Jeff) Lane FlakeSpokesman: Flake’s vote on tax reform will have nothing to do with Trump Trump slams Flake over hot-mic comments: Senator's career is 'toast' Bannon: McConnell 'picking up his game' because of our 'insurgent movement' MORE (Ariz.), Saxby ChamblissSaxby ChamblissLobbying World Former GOP senator: Let Dems engage on healthcare bill OPINION: Left-wing politics will be the demise of the Democratic Party MORE (Ga.), Johnny IsaksonJohn (Johnny) Hardy IsaksonQuestions loom over Franken ethics probe Senate ethics panel resumes Menendez probe after judge declares mistrial Signs of progress, challenges in fighting Alzheimer's MORE (Ga.), Dan CoatsDaniel (Dan) Ray CoatsNational counterterrorism chief to retire at the end of year Former intel chief Hayden: Think twice on a Trump job offer Counterintelligence needs reboot for 21st century MORE (Ind.), Chuck GrassleyCharles (Chuck) Ernest GrassleyFBI informant gathered years of evidence on Russian push for US nuclear fuel deals, including Uranium One, memos show Klobuchar taking over Franken's sexual assault bill Lawyer: Kushner is 'the hero' in campaign emails regarding Russia MORE (Iowa), Susan CollinsSusan Margaret CollinsStates fill family caregiver void left by Congress GOP senator: ObamaCare fix could be in funding bill Collins: Pass bipartisan ObamaCare bills before mandate repeal MORE (Maine), Dean HellerDean Arthur HellerAnother perfect storm: Why we must act before flood insurance runs dry Senators introduce bipartisan gun background check bill Dem PAC bullish on Senate chances MORE (Nev.), Kelly AyotteKelly Ann AyotteExplaining Democratic victories: It’s gun violence, stupid Trump voter fraud panel member fights back against critics Dems plan to make gun control an issue in Nevada MORE (N.H.), Rob PortmanRobert (Rob) Jones PortmanGOP defends Trump judicial nominee with no trial experience Bipartisan compromise is vital to the legislative process Senate GOP reveals different approach on tax reform MORE (Ohio) and Ted CruzRafael (Ted) Edward CruzTexas Republicans slam White House over disaster relief request Dem rep: Trump disaster aid request is 'how you let America down again' Moore endorsements disappear from campaign website MORE (Texas), as well as Democratic Sen. Martin HeinrichMartin Trevor HeinrichSenators introduce bipartisan gun background check bill Dem senator: 'Super close' on bipartisan deal on guns Senators urge DHS to reconsider DACA applications that were delayed in the mail 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. HolderSessions defends Lynch's use of an email pseudonym: 'I have a pseudonym' Holder: Sessions is ‘racially insensitive’ and ‘racially unaware’ Let's start giving media manipulation the attention it deserves MORE will address the issue on Tuesday at the White House, and first lady Michelle ObamaMichelle LeVaughn Robinson ObamaMichelle Obama on sexual misconduct allegations: I’m ‘sick’ Michelle Obama on dealing with difficult times: 'Don't tweet nasty stuff' House passes bill to curb presidential pensions 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.