10:32 p.m. | ANALYSIS: The debate may have produced no clear winner, unlike last week’s presidential contest, but it clarified the differences between the Democratic and Republican tickets. It was a much more vivid and contested discussion. The candidates amplified, if not clarified, the arguments their campaigns have been making in television commercial and speeches. Each candidate made blows and received them. In the end, Biden proved a better spokesman for the Obama administration than Obama did last week, and Ryan proved a more emotional candidate than his budgetary background might have suggested.

-- Michael Kranish

10:29 p.m. | FACT CHECK: 20 million people will lose their insurance under Obamacare: The number represents the upper limit of a projection by the Congressional Budget Office. The most likely scenario, according to the office, is that 3 to 5 million people will be moved off employer-sponsored insurance between 2019 and 2022.

While these people will “lose their insurance” in the sense that they will no longer have the same plans as they did before, many will qualify for Medicaid or government-subsidized private insurance.

Ryan also did not mention that under the 20-million-person scenario, the budget office estimated that the cost of the Affordable Care Act would go down “because the extra costs for Medicaid and exchange subsidies are more than offset by the increased revenues resulting from higher taxable compensation among workers who receive higher wages in lieu of health benefits.”

-- Callum Borchers

10:26 p.m. | FACT CHECK: Obama broke his promise to cut the federal budget deficit in half by the end of his first term: Indeed, Obama pledged shortly after taking office that the deficit would be halved by the end of his first term.

“Now, this will not be easy,” Obama said at the Fiscal Responsibility Summit at the White House on Feb. 23, 2009. “It will require us to make difficult decisions and face challenges we’ve long neglected. But I refuse to leave our children with a debt that they cannot repay, and that means taking responsibility right now, in this administration, for getting our spending under control.”

The deficit in fiscal year 2009 was $1.4 trillion, meaning Obama would have had to shrink the deficit to $700 billion to keep his promise. The deficit was about $1.3 trillion in 2010, 2011 and 2012 and is projected to be about $900 billion in the current fiscal year.

-- Callum Borchers

10:22 p.m. | ANALYSIS: The emotional and personal discussion over abortion is a stark divide. Biden favors abortion rights (as Romney once did) and Ryan is against abortion except in cases of rape, incest and life of the mother. For a significant number of voters, this is an important and determinative distinction.

-- Michael Kranish

10:19 p.m. | FACT CHECK: The Obama administration infringing on religious liberty: The charge generally centers on an announcement by the Department of Health and Human Services in January that virtually all employers would be required to provide free contraception through their health insurance plans under the 2010 national health care law. Churches were exempted, but colleges, charities and hospitals affiliated with religious groups were not.

After strong objections by Republicans and religious leaders, particularly Catholics, Obama outlined a compromise in February: Women employed by religiously affiliated organizations would still receive free contraception coverage, but the coverage would be funded by insurance companies, not by employers.

“No woman’s health should depend on who she is or where she works or how much money she makes,” Obama said in a televised address, announcing the compromise. “As we move to implement this rule, however, we’ve been mindful that there’s another principle at stake here—and that’s the principle of religious liberty.”

“As a citizen and as a Christian, I cherish this right,” Obama added.