Updated: Sept. 1, 4:08 p.m.

President Barack Obama faces growing pressure from within his own party to renounce any benefit cuts to Social Security after comments by the Republican co-chairman of his fiscal commission outraged women’s groups and raised alarms among liberals.

Obama so far is standing by former Sen. Alan Simpson (R-Wyo.) amid demands from liberal groups and a handful of Democratic lawmakers that he resign or be fired following an e-mail he sent to Ashley Carson, the executive director of the Older Women’s League.

In it, Simpson called Social Security a “milk cow with 310 million tits.”

Simpson has apologized, but the episode exposed a growing rift heading into the midterm elections between a White House eager to reach a bipartisan deal on entitlement spending and liberals who see the New Deal-era program as sacrosanct.

Representatives of women’s advocacy groups said on a press conference call Friday that they fear the fiscal commission has been set up to target Social Security for cuts, even though the nation’s spiraling debt has much more to do with the economy, Bush tax cuts and two wars. The advocates said that Simpson has a history of remarks offensive to women and dismissive of Social Security, and they warned Obama that he would be betraying women if he endorses a scheme to slash benefits.

Keeping Simpson as chairman of the panel “sends a message that his behavior is acceptable,” Carson said on the call.

The National Organization for Women has even launched a “Tits for an Ass” campaign asking its members to help buy baby bottle nipples that they plan to send to the White House.

Rep. Raúl Grijalva (D-Ariz.), the co-chairman of the Congressional Progressive Caucus, said that opposition to Social Security cuts has been swelling among the party rank and file who are listening to their constituents, regardless of what the White House and party leaders are saying. “The will of Congress has already shifted in a whole different direction,” he said. “If they are not hearing what I’m hearing then they’re not listening.”

Simpson, however, is not the only member of the panel who has discussed targeting Social Security. House Budget Chairman John Spratt (D-S.C.) in a C-SPAN interview recommended that the commission focus initially on Social Security, and other commission members have mentioned Social Security as one of the areas to target for savings.

Democrats are divided on the issue of whether to trim Social Security benefits to help reduce the deficit; Speaker Nancy Pelosi (D-Calif.) has said she opposes cutting benefits, but Majority Leader Steny Hoyer (D-Md.), a deficit hawk, has floated raising the retirement age as well as trimming benefits for wealthier retirees. That split hasn’t stopped Democratic campaign operatives, including Democratic Congressional Campaign Committee Chairman Chris Van Hollen (Md.), from trying to exploit the Social Security issue by attacking Republicans, including Minority Leader John Boehner (R-Ohio), for proposing a retirement age of 70 and Budget Committee ranking member Paul Ryan (R-Wis.) for proposing an overhaul of the program including private accounts.