About 3 million Americans have now signed up for insurance through President Obama's health care law since the debut of the law's exchanges on Oct. 1, the Department of Health and Human Services said on Friday.

HHS did not specify when the exchanges hit the 3 million mark. Department spokeswoman Joanne Peters replied by email: "We hit 3 (million) this week, don’t have an exact date."

Combined with a previous report by HHS, this suggests that about 800,000 people signed up for insurance between Dec. 28 and sometime this week.

To put this number in context, before the exchanges opened, HHS had been projecting 3.3 million people would enroll by the end of December and about 1.1 million people would enroll this month, bringing the total to 4.4 million by the end of January.

So, this means that January could be the first month in which monthly signups roughly align -- or perhaps even beat -- expectations. Originally, the exchanges were supposed to enroll 7 million Americans through March.

But there's also an important caveat. HHS still hasn't disclosed how many of those who have selected a plan through the health care law have actually paid for it, which is how insurers typically define enrollment.