Updated from June 9

The auto-parts industry is set to meet at the White House this afternoon to ask for as much as $10 billion in further aid, and investors starved for good news in the sector sent supplier shares higher for a second session Wednesday.

The most beaten down stocks -- the companies nearest to default, and therefore with the most to gain from further financial support -- were up the most.

In late morning trading Wednesday, shares of

Lear

(LEA) - Get Report

jumped another 21% to $1.93,

American Axel

(AXL) - Get Report

leapt 22% to $4.35,

Tenneco

(TEN) - Get Report

was up 11% to $10.24, and

Dana Holding

(DAN) - Get Report

gained 16% to $1.76.

Two trade organizations -- the Motor & Equipment Manufacturers Association and the Original Equipment Suppliers Association -- will appeal to the Obama administration's auto task force, and may attempt to meet with members of Congress later in the week.

Specifically, the industry wants to receive $8 billion to $10 billion in guaranteed bank loans. Suppliers are looking at the prospect of dried-up cash flow as

General Motors

( GMGMQ) and

Chrysler

moth-ball factories, or shut them down completely, during their respective bankruptcies.

The trade groups will submit a 71-page proposal to the task force that "clearly demonstrates that immediate action is needed to stabilize the increasingly deteriorating situation in the supply base," according to Richard McKenna, president of the Motor & Equipment group, in a letter appended to the proposal. "Continued employment security and long-term automotive innovation hang in the balance."

Auto-parts suppliers already obtained promises of $5 billion in aid under the TARP program in March. That money took the form of the government guaranteeing Chrysler and General Motors' tabs with parts makers, but parts companies have maintained ever since that $5 billion wasn't enough. Two suppliers have since gone bankrupt:

Visteon

and

Metaldyne

.

The better-capitalized suppliers also saw their stocks rise on the news Wednesday, albeit more modestly.

Federal Mogul

(FDML)

stock was up 2.5% to $10.42;

Magna International

(MGA) - Get Report

rose 3.6% to $39.09 and

Johnson Controls

(JCI) - Get Report

inched higher by less than 1% to $22.03.

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