From the President, this is eminently rational. The core of his fast-dwindling support is the hard left, those who practice the politics of envy and resentment on a regular basis. And there's nothing he and his core supporters would like more than to be able to claim that the results of the 2012 election -- if he wins it -- represent the triumph of collectivism over capitalism. For him it's entirely reasonable to demonize Romney's public sector work; envy and resentment has always been the mother's milk of left-wing politics.
That being said, there are fairly easy lines of rebuttal. To the extent that Mitt Romney helped to create even ONE private sector job, he's far ahead of the President, under whom the unemployment (and discouraged worker) numbers have increased for everyone except government workers. As for that bit about wanting to give out pink slips, seems to me Romney should turn it around by coming up with a clever formulation about how the #1 guy he wants to give a pink slip to is Barack Obama (and the rest of his job-killing, America-distrusting cronies).
Then there's Newt Gingrich, the irrational anti-capitalist. For years now, he has existed (and made his money) by trading on his purported relationships with other Republicans in power, and good-will among the Republican base. His left-wing attacks on Mitt Romney -- which are perfectly positioned to offer the maximum aid to President Obama -- will jeopardize both on a permanent basis. The fact he's doing it anyway manifestly demonstrates that he lacks the stability and fitness to serve as President. Apparently he can't control himself with this, as with much else. (But by doing it to further his own ambition, he makes life more difficult -- not only for Romney -- but for any American who is a believer in, and defender of, the free market.)
Thematically, Romney has plenty of time to explain what's behind these attacks from both Obama and Gingrich. Appeals to division, resentment and envy have always been tried by would-be leaders in tough economic times. They're also the hallmark of failed leaders who desperately want to avert public attention from their own shortcomings.
So when did the politics of "hope and change" (from Obama) and "jobs and growth" (from Gingrich) become the politics of envy, bitterness and resentment? When things went south for each of them.