After having to concede on Day One of Congressional hearings that the solutions it has come up with so far may "not totally" fix the sudden acceleration problem in some of its vehicles, Japanese automaker Toyota faces an even higher profile session with lawmakers today.

Akio Toyoda, the company's president and grandson of its founder, is scheduled to testify before the House Oversight and Government Reform Committee at 11 a.m. ET. You should be able to catch a live webcast of the session here.

On Morning Edition, NPR's Brian Naylor told co-host Renee Montagne that Toyoda is expected to apologize, again, and to get some tough questions from lawmakers who think the company hasn't been forthcoming about the problems. And, Brian says, the National Highway Traffic Safety Administration can also expect more criticism from lawmakers about its response to the Toyota problems:

The Detroit Free Press sums up the news this way:

"Toyota's walk through Capitol Hill's fire pit began Tuesday with more apologies and included a scolding from a Tennessee woman who said she believes only God saved her from a Lexus ES350 that surged out of control in 2006. ...

"Today, President and CEO Akio Toyoda is to tell a second congressional committee that ... 'my name is on every car. You have my personal commitment that Toyota will work vigorously and unceasingly to restore the trust of our customers.' "

And The Washington Post begins its coverage with this:

"Toyota's top U.S. executive told lawmakers on Tuesday that he is not certain the company has fixed its runaway car problems even though it has recalled millions of vehicles around the world."