Screenshot of HealthCare.gov on October 30, 2013
DALLAS (CBSNews.com) -- President Barack Obama asked for a second chance Tuesday for HealthCare.gov. On the first day of a new campaign, the president said the health insurance website is now working for the vast majority of users.
Republicans want to roll back Obamacare, but to that, Obama said, "I will work with anybody to implement and improve this law effectively. If you've got good ideas, bring them to me. Let's go. But we're not repealing it as long as I'm president."
The White House told CBS News that 650,000 Americans visited the website Tuesday. The administration says there were one million visits Monday, and many of the shoppers had better experiences.
Moksha Efsea, a pet-sitter in Fort Worth, Texas, says he had no problem enrolling through HealthCare.gov Monday, a big difference from two months ago.
"I'm a dog walker," he said. "It's a difference between a cooperative, friendly, wagging-tail, happy dog and an angry one trying to bite me. Big difference. Major difference. Struggle versus ease."
Because Efsea has a pre-existing condition -- panic attacks -- he says private insurance would have cost him $800 a month. With a tax credit, his new plan will cost $112.
"Looks like it's going to work out for everyone," Efsea said. "The savings are unimaginable"
In Dallas, LeDawn Stark spent Monday afternoon trying to sign up, too. She's been uninsured for the last three years, and her attempts to log on in October were unsuccessful.
"We're not going back" on health law, Obama says
With HealthCare.gov on the mend, Obama launches new PR push
Shoppers, insurers still face HealthCare.gov hiccups
"I was not even able to get to the point where it told you about the different plans available," Stark said.
She tried to enroll on the revamped site and said it was "far better."
But a few minutes later, a problem occurred. The system did not recognize her son's Social Security number and she could not go forward.
"I'm going to call them, and we're going to get to the bottom of this, because I need to get this done," Stark said.
LeDawn Stark tried setting up an account by phone Tuesday but still was not able to finish the enrollment process. She says she's going to try again in a few days.
© 2013 CBS Interactive Inc. All Rights Reserved.