Supporters of the rules say they are essential for protecting a vibrant Internet, free of discriminatory gatekeepers. They are concerned that without the regulations, Internet providers could block or slow down websites that fail to pay special fees or that are viewed as a competitive threat.
But critics consider the rules an illegal power grab that burdens businesses.
Verizon sued to overturn the rules, arguing that the FCC overstepped its legal authority to regulate the Internet.
The U.S. Court of Appeals for the D.C. Circuit is currently considering Verizon's lawsuit and is expected to issue a decision this year.
A net-neutrality bill would put the FCC's rules on firmer legal ground, but the measure would face long odds in Congress.
Republicans are vocally opposed to net neutrality regulations, and the House voted to repeal the FCC's order in 2011. As long as Republicans control the House, a net-neutrality bill would be unlikely to pass.
In her speech, Eshoo said she hopes her subcommittee will give "serious consideration" to updating video regulations.
She said the Internet has revolutionized how people consume video content, but expressed concern that cable providers, which offer both Internet service and cable TV packages, might try to limit competition from websites.
"I want to ensure constituent companies like Netflix continue to grow and are not hindered by discriminatory data caps or other tactics that deny consumers the freedom and flexibility to stream video content whenever and wherever they want," the Silicon Valley lawmaker said.