The Obama campaign’s new ad ruffles my feathers.

It’s not the message per se. The Big Bird spot fairly points out that Mitt Romney seems more interested in cracking down on “Sesame Street” than on Wall Street. The problem is President Obama has, to mix animal metaphors, taken the bait — and he’s pursuing a red herring.

Big Bird is not the problem. The problem is Snuffleupagus.

The threat presented by Romney’s budget is not in the few cuts he has specified but in the vastly larger amount of unseen cuts he has yet to identify.

At the Denver debate, Romney said he would eliminate Obamacare (doing so would actually increase the budget deficit, because of related tax hikes) and the public-broadcasting subsidy, which is $445 million a year — or little more than one one-hundredth of 1 percent of federal spending. But Romney proposes to cut federal spending by trillions of dollars — more than $5 trillion over the next decade, assuming he follows the sort of blueprint laid out by his running mate, Paul Ryan. That threatens much more than Muppets and monsters. Human lives are at stake.

As if to remind us of this, Rep. Darrell Issa, the indefatigable Republican chairman of the House Oversight and Government Reform Committee, has called a hearing for noon Wednesday even though Congress is in a weeks-long recess. The emergency cause for the hearing? Probing “The Security Failures of Benghazi” — lapses in diplomatic security that led to the deaths of Ambassador Chris Stevens and three other Americans in Libya.

The purpose of the pre-election hearing, presumably, is to embarrass the administration for inadequate diplomatic security. But Issa seems unaware of the irony that diplomatic security is inadequate partly because of budget cuts forced by his fellow Republicans in Congress.

For fiscal 2013, the GOP-controlled House proposed spending $1.934 billion for the State Department’s Worldwide Security Protection program — well below the $2.15 billion requested by the Obama administration. House Republicans cut the administration’s request for embassy security funding by $128 million in fiscal 2011 and $331 million in fiscal 2012. (Negotiations with the Democrat-controlled Senate restored about $88 million of the administration’s request.) Last year, Secretary of State Hillary Clinton warned that Republicans’ proposed cuts to her department would be “detrimental to America’s national security” — a charge Republicans rejected.

Ryan, Issa and other House Republicans voted for an amendment in 2009 to cut $1.2 billion from State operations, including funds for 300 more diplomatic security positions. Under Ryan’s budget, non-defense discretionary spending, which includes State Department funding, would be slashed nearly 20 percent in 2014, which would translate to more than $400 million in additional cuts to embassy security.

The Romney campaign argues that such extrapolations are unfair, because Romney and Ryan haven’t specified which programs they would cut and by how much. And that’s the problem: The danger in Romney’s plan is not in the few cuts he has detailed but in the many he has not.

If Romney follows through on the tax cuts he has endorsed, increases defense spending by $2.1 trillion over a decade as promised and maintains Social Security and Medicare as they are for those 55 and older, he’d need to cut everything else government does by nearly a third — or more than $200 billion — in 2016. By 2022, the liberal Center for American Progress calculates, such government functions, including the State Department, would be cut by 53 percent. The $445 million Romney saves by axing PBS will get him less than half of 1 percent of the way toward the budget cuts he would need to make by 2016.

Obama is making a mistake in allowing the discussion to be about Big Bird, which he continued to do on Monday, telling supporters that “Elmo has been seen in a white Suburban” (apparently a botched reference to O.J. Simpson’s white Bronco). His new campaign ad, likewise, has a cute punch line: “Mitt Romney, taking on our enemies, no matter where they nest.”

Obama would do better to focus on Big Bird’s elephantine friend Aloysius Snuffleupagus. For years, Big Bird tried to convince the skeptical grown-ups on “Sesame Street” that his “imaginary” friend was real. Finally, after concern that the grown-ups’ dismissal of Big Bird’s truthful claim might dissuade children from reporting sexual abuse, “Sesame Street’s” producers made Snuffy visible to the grown-ups.

In the presidential campaign, Big Bird is a distraction from Romney’s real cuts, which he is not yet allowing Americans to see. Obama should be drawing attention to the elephant in the room.