Story highlights

President Obama promises that the site will work well

But officials declined to say if there were any glitches reported

The new enrollment period opened Saturday

In general, rates higher

(CNN) —  

The Obama administration went into the first hours of the new enrollment period under the Affordable Care Act with confidence that last year’s problems with were behind them.

“We’ve spent the last year improving and upgrading, to make it faster and easier to use,” President Barack Obama said in his weekly address as the enrollment period launched Saturday morning.

Health and Human Services Secretary Sylvia Burwell said that more than 23,000 people submitted an application in the first eight hours of enrollment and more than 1.2 million unique visitors shopped for coverage on last week.

There were reports, including from USA Today, of some glitches in the enrollment process. When asked by CNN whether applicants were having any problems with the website, officials declined to comment.

Depending on where they live, consumers are finding premiums that have increased or decreased, according to new data released by the Centers for Medicare & Medicaid Services.

The change in premiums differs widely state to state, according to multiple independent consulting firms that analyzed the data.

In Alaska, the average lowest bronze plan premium increased 28% and in Mississippi, the same plan’s premium decreased 19%. On average, states saw a 3-4% increase in premiums, according to Avalere Health, a research and consulting firm.

“The bottom line is that exchange enrollee’s 2015 premiums will vary widely based on geography,” Elizabeth Carpenter, director at Avalere Health, said in a press release.

A separate study by PriceWaterhouseCoopers – which analyzed 43 states and the District of Columbia – found that premiums are rising 5.6% on average.

The administration has not released an official number on the change in premiums.

As a new enrollment period for Obamacare begins, Republicans are not shying away in their fight to put an end to Obamacare.

“Conservatives should… take advantage of opportunities to repeal any part of the law and replace it with better policies that empower Americans, not Washington,” Utah Republican Sen. Orrin Hatch wrote in USA Today this week.

Wyoming Republican Sen. John Barrasso, an orthopedic surgeon and health policy expert, said that GOP hopes of repealing Obamacare are not realistic until there is a Republican in the White House. But he told WPBI radio last month conservatives should “systematically strip away the worst parts of Obamacare.”

But some conservatives want a more radical approach, and recommend repealing Obamacare by using the budget tool reconciliation, which requires only 51 votes and, ironically, was used to pass the law in 2010.

Administration officials are continuing to encourage signups, claiming there will be more affordable choices for 2015.

“This window won’t stay open forever. You only have three months to shop for plans, so it’s worth starting right away. And it might make a big difference for your family’s bottom line,” Obama said in his weekly address.

At the start of last year’s rollout, was plagued with technical issues, preventing consumers from purchasing insurance, which the Obama administration ascribed to “glitches” due to high traffic on the site.

According to the Centers for Medicare & Medicaid Services, there is a 25% increase in issuers in the marketplace and more than 90% of consumers will be able to select from three or more issuers.

“Today’s data provides further evidence that the Affordable Care Act is working to improve competition and choice among Marketplace plans in 2015,” CMS Administrator Marilyn Tavenner said. “Consumers should shop around, with new options available this year they’re likely to find a better deal.”

More than 7 million people enrolled in insurance through the Affordable Care Act and paid an average of $82 a month, according to the Obama administration.

A Gallup poll released Friday found that over seven in 10 Americans who bought health insurance policies through the government exchange rate the quality of their healthcare as “excellent” or “good.”

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CNN’s Stephen Collinson and Kevin Bohn contributed to this report