In their defense of their policies Thursday, President Obama and Vice President Joe Biden sometimes took license with the facts or left out important information. Here are highlights:

The claim about the deficit and spending: "Independent analysis shows that my plan would cut our deficits by $4 trillion. Last summer, I worked with Republicans in Congress to cut $1 trillion in spending." Obama

The facts: President Obama repeated a claim made by former President Bill Clinton the night before, but even less accurately. Clinton referred to a "plan of $4 trillion in debt reduction over a decade." Obama leaves off the time, and makes it sound like the current $1 trillion deficit would be eliminated. While the numbers seem large, the results are unimpressive. At the end of the 10-year budget window, Obama would have the national debt at a 76.5 percent of gross domestic product. That would be an increase over the 74.2 percent of GDP in this year. In contrast, the debt reduction plan envisioned by the Simpson-Bowles commission -- cited by the president -- would reduce that ratio close to 60 percent.

The claim about Social Security: "We will keep the promise of Social Security by taking the responsible steps to strengthen it -- not by turning it over to Wall Street." Obama

The facts: Obama's rival, Mitt Romney, briefly supported private accounts as part of Social Security in the 2008 campaign but no longer does. In his 2010 book, "No Apology," Romney makes it clear that the 2008 stock market turmoil had changed his thinking on the issue. He concluded that mandatory private accounts won't work. The plan he supports now is similar to what then-Vice President Al Gore proposed in the 2000 presidential campaign, what Gore dubbed "Social Security Plus." Gore said the accounts would be voluntary and "not be the product of any reduction or diversion of Social Security revenues."

Meanwhile, Obama's recent budgets have had limited Social Security reforms.

The claim about Detroit: "He [Romney] was willing to let Detroit go bankrupt." Biden

The facts: This statement is drawn from a headline -- "Let Detroit Go Bankrupt" -- on an opinion article Romney wrote for the New York Times. But he did not say that in the article, but repeated it on television.

Although "bankrupt" often conjures up images of liquidation, Romney called for a "managed bankruptcy." This is a process in which the company uses the bankruptcy code to discharge its debts, but emerges from the process a leaner, less leveraged company. Ultimately, GM and Chrysler did go through a managed bankruptcy -- along with getting nearly $80 billion in loans and other assistance from the Bush and Obama administrations. But many analysts have concluded that taking the approach recommended by Romney would not have worked in 2008, simply because the credit markets were so frozen that a bankruptcy was not a viable option at the time.

The claim about exporting jobs: "As a matter of fact, he has a new tax proposal -- the territorial tax -- that experts say will create 800,000 jobs, all of them overseas." Biden

The facts: Biden is quoting from a disputed study. At issue is a Romney proposal, as part of a corporate tax reform, to allow foreign profits by corporations to be exempt from domestic tax. The Simpson-Bowles deficit-reduction Commission recommended such a system in its report. The study cited by Biden, which appeared in Tax Notes, did not actually study Romney's plan. Moreover, it said that such a system would create 800,000 jobs overseas, but not necessarily at the expense of U.S. jobs if unemployment rates are low.