Dwight Eisenhower was US President the last time GM shares were so low
GM shares have fallen to a 54-year low as investors worry about the firm's financial position amid falling sales and high debt levels.
GM and other US car giants release June sales figures on Tuesday, expected to show a continued slump in US demand.
Soaring petrol prices have turned US drivers away from large, fuel-intensive vehicles, once prioritised by GM, in favour of smaller and crossover cars.
GM shares fell as low as $11.12 on Monday, their lowest level since 1954.
Their value has plunged 35% in the past month as analysts fret over the progress of GM's cost-cutting plan and suggestions it may need to issue new shares to raise cash.
Analysts expect June's data to provide little consolation for GM, whose US market share is continuing to decline.
Total sales in GM's home market fell 30% in May, with truck sales particularly weak.
Sales had fallen 22% in April, although strong sales outside the US meant that global sales in the first quarter were only 1% lower than in 2007.
GM acknowledged recently that soaring petrol prices were "changing consumer behaviour" and pledged a greater focus on smaller, more fuel-efficient models.
As a result, GM is reviewing the future of its Hummer sports utility vehicle brand as well as cutting thousands of jobs and closing plants across North America to save money.
"The situation is very serious for GM," said Rebecca Lindland, an analyst at Global Insight.
"Cash is very limited for everybody and when you couple the very tight credit and combined with very poor auto sales, it just aggravates the difficult situation."
GM has lost a combined $51bn over the past three years and recently said it would not return to profitability, as previously hoped, in 2008.
Should GM shares continue to slide, experts have said the firm is in danger of falling out of the Dow Jones Industrial Average index of leading US stocks.
GM has been a member of this prestigious club since 1925.