A little more than a month into Obamacare's second-ever open enrollment period, at least 6.4 million people have already signed up for 2015 health plans, the Obama administration announced earlier this week. That number includes 1.9 million people who are first-time customers on HealthCare.gov, the federal enrollment portal serving 37 states. But as I wrote last month, a number of Obamacare advocates say the administration picked a really tough season to hold open enrollment.

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The Obamacare enrollment period just re-opened, but the Obama administration is already starting to lay down new ground rules for how enrollment will work in the future. Among the ideas: changing when the enrollment period will actually take place. And that could have big implications for how many people will sign up for coverage.

The law's first ever enrollment period ran a lengthy six months, from Oct. 1, 2013 to March 31. The second enrollment period now underway will be half as long — it started on Nov. 15 and is scheduled to end Feb. 15. Starting in fall 2015, the Obama administration says enrollment in the law's health insurance marketplaces, or exchanges, will run Oct. 1 through Dec. 15 of each year.

What's the point of shifting up the dates? It's all about eliminating possible confusion about when a person's coverage actually starts, according to the proposed rule issued Friday afternoon by HHS. In the future, all health plans purchased in the enrollment window will start on Jan. 1 of the following year, which is a change from how things work now. Under the current enrollment window, if you purchase a plan on Dec. 15, your coverage starts start Jan. 1. But if you purchase a health plan on Dec. 16, you have to wait until Feb. 1 for your coverage to kick in.

"This will be less complicated for Exchanges and issuers to implement," HHS wrote about the proposed change.

But there are some experts who think that having people sign up for health insurance during the fall is a bad idea in the first place.

"[L]ate fall is one of the most financially and emotionally stressful times of the year, particularly for people with limited incomes," wrote Harvard School of Public Health professor Katherine Swartz and John Graves, an assistant professor at the School of Medicine at Vanderbilt University, this past summer in Health Affairs. "The holiday season between Thanksgiving and New Year’s — with pressures for buying presents, travel, and the onset of winter home-heating bills — strains many family budgets. These are not months when lower-income households have extra money for paying premiums for health insurance plans that begin the following January."

Some Affordable Care Act advocates and tax preparers like Jackson Hewitt have also been urging the Obama administration to set an Obamacare enrollment period that more closely aligns with tax season, citing a few reasons. People in tax season will learn whether they're paying the ACA penalty for not having health insurance, so they may make the calculation they'd rather get coverage. Also, people receiving tax refunds may then feel like they have the financial flexibility to purchase private coverage.

The advocacy group Families USA, one of the ACA's strongest proponents, has also called for a marriage of the enrollment period and tax season. "Fully aligning the open enrollment period with the tax filing period would significantly increase enrollment," the group asserted in recommendations issued earlier this year.

The important caveat here is that HHS has only proposed the change so far and is asking for feedback on this provision, among others. But given the importance of the enrollment window and those who've spoken up, it will be interesting to see if this rule sticks.