Health and Human Services Secretary Kathleen Sebelius said as much herself: "You are not fully enrolled [in Obamacare] until you pay your premium." Yet data collected by the Republican-led House Energy and Commerce Committee shows that as of April 15, just 67 percent of enrollees in the federally-run Obamacare marketplace had paid their first month's premiums.

There are a variety of factors that explain why more than 30 percent of enrollees have yet to pay. To begin with, it's worth noting that millions of Americans waited until the final weeks and days of the open enrollment period (which closed on March 31) to sign up for Obamacare. Many were allowed to finish the enrollment process after March 31, due to the flexibility the Obama administration granted. Consequently, many Americans on the new marketplace simply didn't owe any premiums by April 15.

"Americans are not in the habit of paying something earlier than they have to," said Tim Jost, a consumer advocate and professor of health law at Washington and Lee University.

Even so, the nature of the individual health insurance market -- factors like the fluidity of the marketplace and consumers' lack of familiarity with the system -- make it difficult to collect premiums from all enrollees.

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Marc Boutin, executive vice president of the nonprofit National Health Council, said that getting nearly seven in 10 enrollees to pay just two weeks after the open enrollment period closed "seems quite positive." While more comprehensive data will come in later, he called it "a really good indication of the direction we're going."

"You have to recognize it's a new payment for many people, and it's not uncommon for people to miss that first payment or be confused about when to pay it," he said. From here, "I think the numbers are just going to go up."

Even so, it's unlikely the Obamacare marketplace will ever get 100 percent of its enrollees to pay their first month's premium. In 2013, before the Obamacare marketplace existed, about 90 percent of enrollees in the individual marketplace paid, Jost said.

"There's quite a bit of mobility between the individual insurance market and Medicaid and the employer-based market," he pointed out. Indeed, a recent study showed that before the Obamacare marketplaces were implemented, just 42 percent of people on the individual market kept the same plan for more than a year. It's likely that a portion of Obamacare enrollees found better coverage through an employer or somewhere else and decided not to make payments for their Obamacare coverage.

Those who do want to pay for their Obamacare coverage may not have a convenient way to do so.

"A high proportion of the people that are low-income and uninsured don't have checking accounts, don't have credit cards," Jost noted. "One thing Congress could do to help out, or the insurers could do, is create ways for people to pay their premiums in cash."

Some insurers are addressing that problem by partnering with CVS/pharmacy, which recently announced it's establishing a program to enable people to pay their insurance bills at CVS cash registers. Jost also noted that the Affordable Care Act does require insurers to accept debit card payments, which should help customers.

"This is a real problem that needs to be worked on as we draw more and more people into the insurance system that aren't in the traditional economy," Jost said.

Boutin noted that getting a higher portion of enrollees to pay premiums should be achievable: "You have to recognize the insurance companies obviously have a vested interest in having people pay," he said. "And obviously the people who enrolled have a vested interest" in keeping their insurance.

Still, policymakers can decide how much they want to facilitate that process. In Georgia, for instance, Republican Gov. Nathan Deal on Wednesday signed a bill prohibiting the state from spending any money to help citizens enroll in Obamacare.

A new report from the Robert Wood Johnson Foundation suggests that a state's support could make a difference. The report compared five states that partnered with the federal government to implement its Obamacare marketplaces and found that Illinois spent the least amount per person on efforts to assist enrollees. The data collected by the Energy and Commerce Committee, meanwhile, showed that of those five states (Illinois, Delaware, Arkansas, New Hampshire and West Virginia), Illinois had the smallest portion of enrollees who had paid their first month's premiums.