The Washington Post should have found someone who would have pointed out President Obama's misrepresentation when it quoted him saying:
“Government can’t stand on the sidelines in our efforts [to reduce inequality and increase mobility], because government is us. It can and should reflect our deepest values and commitments.”
Of course government has not been on sidelines, it has pursued policies that increase inequality. There are a long list that fall into this category including the bank bailouts of 2008-2010, too big to fail insurance for large banks, stronger and longer patent and copyright protection, and a trade policy that puts less educated workers in direct competition with low paid workers in the developing world, while largely protecting the most highly paid professionals, like doctors, from the same sort of competition.
However the biggest way in which the government has promoted inequality is by running budgets that lead to large scale unemployment and underemployment. Just as the decision to deliberately use fiscal policy to stimulate the economy and create jobs is a policy choice so is the decision to run smaller budget deficits, thereby reducing growth and employment. The government is currently following the latter policy denying work to millions of people. Also, since the bargaining power of workers in the bottom third of the labor market depends hugely on the level of unemployment, the high unemployment policy is also reducing their wages.