SAVANNAH, Ga. — A senior aide to Sen. Bernie Sanders on Sunday characterized Hillary Clinton’s latest tax plans as “tentative half-steps that sound Republican-lite,” escalating the sparring between the Democratic presidential campaigns over their respective commitments to helping the middle class.

“Given the disappearing middle class and massive income wealth inequality in America today, we clearly have to go a lot further than what Secretary Clinton proposes,” Sanders’s communications director, Michael Briggs, said in a statement issued Sunday night as Sanders campaigned here.

The statement came in response to a pair of initiatives put forward by Clinton on Sunday that would benefit people who care for an elderly parent or other family member. The former secretary of state is proposing a tax credit that would defray up to $1,200 in out-of-pocket expenses, as well as changes to the Social Security system to allow credit toward a wage earner’s monthly benefit at retirement when that person takes time off to care for an elderly relative.

As part of an ongoing rollout of measures aimed at bolstering the middle class, Clinton also has previously proposed tax credits for college costs and large out-of-pocket medical expenses.

Her campaign, in turn, has recently attacked Sanders for his support of measures that would raise taxes on the middle class. Until recently, both camps had attempted to make a virtue of not talking about the other.

Sanders is advocating for a single-payer “Medicare for all” health-care system. Under legislation he previously introduced, his campaign acknowledges that taxes would increase on the middle class, but his aides argue that the overall cost of health care to would be lower because people would no longer pay premiums or deductibles.

Sanders also backs a bill pending in Congress that would mandate employers provide paid family leave time after a child is born. The bill would be funded by an increase in payroll taxes estimated to cost the average worker about $72 a year.

Speaking at LeMoyne-Owen College in Memphis, candidate Hillary Clinton discusses college-related debt, the president's healthcare law and prescription drug pric (Reuters)

Clinton has spoken out forcefully for the concept of paid family leave but not embraced the particular measure because it violates a campaign pledge not to raise taxes on families making less than $250,000.

During a campaign rally here that drew close to 2,600 people, Sanders touted the bill, which is sponsored by Kirsten Gillibrand, Clinton’s successor as a senator from New York. Sanders made a similar pitch earlier in the day during a stop in Saint Helena Island, S.C., where he said the bill is widely supported by progressives in Congress, with 20 co-sponsors in the Senate and 113 who have signed on to a similar measure in the House.

“That’s a lot,” said Sanders, who then repeated a challenge he has extended to Clinton to join those supporting the legislation, which he said would cost the typical worker $1.39 a week.

Sanders also talked up his support of a plan to expand Social Security benefits by increasing taxes paid into the program by those who earn more than $250,000 a year. Clinton has said she is willing to consider the idea but has not committed to “scrap the cap,” as progressive activists call the plan.

Sanders's stop here Sunday night followed three days on the ground in South Carolina, the first state in the South —where Clinton has a large lead in the polls — to hold a primary election.

Earlier Sunday, Sanders visited a pair of African American churches in North Charleston. African Americans are expected to comprise half the Democratic primary electorate next year, and Sanders, by his own admission, is not particularly well known among black voters.