One of the health-care law’s biggest challenges doesn’t come from the courts. It’s not a Congressional attack, nor is it any budget cut that may emerge  the debt-ceiling debate.

Instead, it’s a huge logistical obstacle: making sure all the people who are supposed to gain insurance coverage actually sign up.

The Congressional Budget Office estimates 34 million people will gain insurance under the health-care law by 2021. No one gets dropped into any default program; everyone will have to enroll in coverage. Some will go into Medicaid, others will purchase on exchanges (often with a federal subsidy), and still others will buy a completely private option.

The struggle has already started. Last summer, the law created high-risk insurance pools, meant to serve those with pre-existing conditions who have had trouble finding coverage. A program that many expected to be flooded has has seen dismal enrollment. The administration has lowered premiums as a way to entice new enrollees; at last count, just about 12,437 Americans had signed up.

All this begs the question: How do you enroll 34 million Americans, many dealing with insurance for the first time?

A study released Thursday suggests that many clues could exist in the Children’s Health Insurance Program, or CHIP. Created in 1997, CHIP is a state-federal partnership that provides health insurance coverage for lower-income kids and their families.

Over the past decade, CHIP enrollment has steadily increased. More and more of the kids who are eligible actually sign up for coverage. New numbers from the Robert Wood Johnson Foundation show that, as of 2009, CHIP covers about 84.9 percent of eligible children--a very high number for a means-tested program. That’s also a slight uptick in the rate of coverage, even with 2.5 million new children becoming eligible that year.

Because of CHIP, the number of children with insurance has actually been increasing for years now. In 2008, we had the lowest rate of uninsured kids since the Census bureau started collecting data in1967. It’s a positive trend that often gets masked by population-wide declines in rates of insurance.

What does CHIP do to get kids enrolled? It all revolves around reducing red tape. Eliminating face-to-face enrollment interviews, for example, significantly increases enrollment numbers. Allowing for renewal of benefits by mail, rather than in person, helps too. Pre-populated enrollment forms, where a lot of a beneficiary’s information is already filled out, are currently being tested. In total, anything that makes it easier to sign up tends to increase enrollment. And that’s going to be key to moving 32 million people into an insurance system pretty soon.

One other thing we can learn from CHIP: enrollment levels could end up varying widely by states, and how many of these streamlining strategies they use. In Vermont, 92.4 percent of eligible kids are enrolled in CHIP; in Nevada, only 62.9 percent are. The disparities show just how much can hinge on how states decide to structure their enrollment processes.