Is Sen. Elizabeth Warren running for president?

There was urgency in Massachusetts Sen. Elizabeth Warren's voice when she said she wouldn't be running for president in 2016.

"We have to make changes right now," the Democratic senator said Tuesday on "CBS This Morning," repeating the words "right now" four times in the span of a minute.

"You can ask this in a whole lot of different ways, but the key is -- I'm not running for president," she said again.

While some Democrats have been pushing for her to run for presidency, she said she wants to focus on what's currently happening in the Senate. Just over a year into her first term, Warren has continued to hammer away at the theme of the middle class.

"Maybe it's because, like a lot of families, I grew up on the ragged edge of the middle class," she said.

In her new memoir, "A Fighting Chance," Warren describes how her life experiences shaped the person and senator she is today.

Warren was 12 years old when her father had a heart attack, and she remembers how it impacted her family financially. Her father ended up working as a maintenance man, and her mother worked for minimum wage at Sears, she said.

"But I made it to the United States Senate, and I made it to the United States Senate in part because America was back then investing in kids like me."

She said she went to a commuter college that cost $50 a semester.

"Today, that's not happening. Today it's a rigged playing field, and it's not working," Warren said. "Washington is not working for hard-working middle-class families."

Working with her co-authors, she researched what set middle-class families who went bankrupt apart from those who didn't.

"What we discovered is that those families mostly look like the rest of middle-class America -- went to school, bought homes, got married, had kids -- but the difference was they got totally slammed by a serious medical problem, had a long period out of work, or had a death in the family or a divorce."

Those types of factors accounted for more than 90 percent of all bankruptcy filings, she said.

"It was like it was in my family -- you can work hard, you can play by the rules, and you can still take a terrible smack to the head financially."

With the income inequality gap growing, she gave the example of the banking system to explain why she thought "the game" was fundamentally rigged.

The government bailed out those institutions and some financial reforms were put in place, "but look where we are today. Those CEOs of the largest financial institutions still strut around Washington. Those big banks still push back on regulators and block real change," Warren said. "Today those large financial institutions are 38 percent bigger than they were when we bailed them out, and they break the law and nobody goes to jail. That's not a level playing field. That's not a fair system."

She said the answer to the problem is more regulation and tax reforms since Washington works for "those who can hire an army of lobbyists and an army of lawyers," not regular families.

"If we don't make that fundamental change, we're just going to live in a world where the rich keep getting richer, the powerful keep getting more powerful, and everybody else falls behind."

Warren highlighted a couple of specific areas she'd like to see progress on.

"I'm out here working on the issues we need to work on right now, and I got to say, we need to refinance the student loan debt that's outstanding. We need to raise the minimum wage. We need to secure social security, and we need to hold those big financial institutions accountable. And we need not to put that off."