President Obama sharply defended his signature health care law again on Tuesday, arguing “this law is working” and promising he would continue to oppose any Republican efforts to dismantle it.

“I’ve always said I will work with anybody to implement and improve this law effectively. You got good ideas? Bring them to me. Let’s go. But we’re not repealing it as long as I”m president,” Obama said at an event at the White House.

Here’s a closer look at where the law stands, two months after the rollout of its biggest part, the attempt to expand health insurance to millions of Americans.

1. The website is better, but far from perfect

In October, it was hard to find anyone in the country who was able to navigate HealthCare.gov, the website that residents of 36 states use to enroll in Obamacare. That’s no longer the case. Administration officials told NBC News about 100,000 enrolled in private health care plans through HealthCare.gov in November, a huge jump from the 27,000 in October.

That said, it’s still not clear if the website can handle large amounts of users at the same time, and this could be a major problem. While it is difficult to quantify this, I and other reporters covering the health care law spoke to people yesterday who went to HealthCare.gov only to have the site inform them it was too crowded with users. This was after the much-hyped overhaul of the site ahead of December 1.

Administration officials note there is now a system set up in which HealthCare.gov will send you an e-mail when the site has less traffic, but the problem remains the same: some people who want to purchase health insurance can’t because of a website that is not performing as well as was originally hoped.

“I imagine a lot of people are trying out the system today, so I’m hoping the delay is temporary, but it is a bit frustrating to have waited until we received the green light that the site was ready for use and to be back with no access,” an Obama supporter who lives in Georgia and has tried to enroll in HealthCare.gov for weeks told me yesterday via e-mail.

A crush of users are expected in the week leading up to Dec. 23, the last day someone can sign up for health insurance that starts on January 1. (If you enroll after that day, your coverage would start on February 1.). And that could turn into a repeat of October 1, when almost no one could enroll through the site.

Obama administration officials have already conceded they are not totally confident in the website, as they told pro-Obamacare groups in private meetings over the last two weeks not to have huge organizing events that would send thousands of people to the website and potentially flood it.

Health and Human Services Secretary Kathleen Sebelius has urged people to try use HealthCare.gov on weekends, mornings and evenings, an acknowledgement that in the middle of a weekday, it may hard to use the site.

And another huge issue remains. Some insurance companies are saying the website isn’t properly sending them data about what people have signed up for. Until you actually pay the first month’s bill to the insurance company, your insurance does not kick in. And it’s unclear exactly how many of the tens of thousands who have completed the process on HealthCare.gov have received confirmation from an insurance company and are on their way to getting a bill, paying it and receiving a list of doctors they can visit.

2. Enrollment is growing and has crossed the 1 million mark 

There are three groups who are enrolling in the heath care plans under the law. Many with low incomes (below $32,000 for a family of four) are newly eligible for Medicaid, and some who did not know they qualified for the program before and had not enrolled are doing so now.

Second, people who were previously uninsured are enrolling in private plans under the law for a number of reasons: the federal mandate requires most Americans get insurance, some people who had illnesses before faced either very high prices or no insurance options at all under the pre-Obamacare system, and insurance is more affordable for some healthy Americans because of the new subsidies under the  law.

A third group that is enrolling contains people whose previous health care plans did not comply with Obamacare’s new rules for insurance. (President Obama last month said states and insurance companies could keep some of these old plans in place, but not many states have accepted that option so far.) These people are not newly insured, but are now getting insurance through the Obamacare system.

The data from October showed that about 27,000 people enrolled in private health care plans through HealthCare.gov, around 70,000 in states that have their own websites. And Obama administration officials announced on Tuesday that more than 700,000 people have been deemed eligible for Medicaid under the Obamacare rules, as well another 700,000 who were eligible before but didn’t enroll in the program.

So more than 1 million Americans who didn’t have health insurance before the start of October now have it.

The CBO last year estimated 7 million Americans would get private insurance through the Affordable Care Act, and another 9 million would be newly eligible and enroll in Medicaid or the State Children’s Health Insurance Program by next year.

Signups for the new health insurance options are behind that pace so far, although Obama aides note they expect a surge of applications both at the end of December and in March, when the enrollment period ends and people who don’t get insurance will face fines.

But 1 million is already a very large number.

3. The youth remain a mystery

Obama aides said earlier in the year their goal was that if 7 million people enrolled in the new private health care plans,  2. 7 million would be between between ages 18 and 35.

Administration officials say that getting a large percentage of young people into the private insurance plans is a more important goal than reaching 7 million insured, because it would reassure insurance companies that the new enrollees are not all old and/or sick, and therefore more expensive customers. The administration would be excited, for example, if 5 million people were newly insured in private plans,  2.5 million of whom were between ages 18 and 35. (Obama aides would not tell me if there is an exact percentage of young people that they must have, but 2.7 million is 39 percent of 7 million.)

So far, it’s very hard to tell how young the new enrollees are. The administration has not released that data for the people who have signed up through HealthCare.gov, a sign that enrollment among the young is not going as well as hoped. (If half of the enrollees were between 18 and 35, Obama would be trumpeting that fact loudly.)

On the other hand, Kentucky reported that in October, 40 percent of its enrollment was from adults under 35, hitting the administration’s target.

Overall, it’s just too soon to make judgments about the number of young people enrolling in the health care law.