Warren, in her first standalone Senate bill, is pushing to set the interest rate for subsidized loans equal to the rate that banks use to borrow from the Federal Reserve: just 0.75 percent.
"These are the same banks that cost millions of Americans their jobs and nearly broke the economy," she said on a call with supporters organized by MoveOn.
"It's a crisis that hurts everyone," Warren added. "When young people are struggling to pay huge student loans it undermines their financial security but it also prevents them from buying homes" and other spending that keeps the economy thriving.
Last month, a report from the Consumer Financial Protection Bureau, which Warren helped create, estimated that the fallout from high student loan debt could be hurting the economy by up to $100 billion.
In the call on Monday, Warren said that addressing the July 1 deadline was just a "foot in the door" to make larger changes to tackling student loans. She also wants to address private student loans and the rising price tag of higher education.
"It's not enough just to deal with student loans," she said. "We have got to attack the rising cost of college head on."
In May, the House passed a bill to permanently tie the interest rate to the 10-year Treasury note, plus 2.5 percent. Warren rejected that bill as "a system under which the federal government would profit even more."