Harris's comments to the Senate Health, Education, Labor and Pensions Committee were met with praise from Democrats on the panel.
"The minimum wage has not kept up as the rest of the economy has moved forward," said Chairman Tom Harkin (D-Iowa).
Sen. Lamar Alexander (Tenn.), the top Republican on the committee, dismissed the notion.
"From my point of view, and I think the point of view of many on our side of the aisle, what the minimum wage is is a good-sounding attempt to fix the price of labor," he said. "In a market system what that usually does is create a shortage. It creates less."
This year, Harkin and 30 other senators introduced the Fair Minimum Wage Act, which would gradually increase the minimum wage from its current $7.25 to $10.10 per hour and peg it to inflation.
"This modest increase, which is well in line with previous increases throughout history, will give 30 million Americans a higher paycheck, including the parents of 18 million children," he said.
President Obama has also proposed raising the wage. In his State of the Union address this year, he supported a $9.00 an hour minimum wage, which would also be tied to inflation.
In an event earlier on Tuesday afternoon to commemorate the 75th anniversary of former President Franklin Roosevelt's signing of the Fair Labor Standards Act, which created the minimum wage and 40-hour work week, Vice President Joe Biden said raising the wage would have a "ripple effect" on other earnings.
"The rate hasn't increased for 20 years," he said. "We're going to fix that."
The proposals in Congress and from the president would also raise the minimum wage for tipped employees like waiters, who currently make $2.13 an hour.