By David Morgan and Caren Bohan

WASHINGTON (Reuters) - The race intensified on Monday between Republicans trying to discredit President Barack Obama's signature healthcare law and officials trying to repair the flawed website crucial to the success of his policy reform.

While Obama administration officials said they had made significant improvements to HealthCare.gov, Republicans began appealing to the public on Monday for personal accounts of negative experiences with the Affordable Care Act, commonly called Obamacare.

The government has promised the site will be operating smoothly for the vast majority of users by November 30, so that potentially millions of people can enroll by a December 15 deadline for coverage that would begin on January 1.

"Eventually it's going to be the easiest place to shop for healthcare," Obama told a call on Monday put together by Organizing for Action, the group that grew out of his 2012 re-election campaign.

Obama said the site was getting better every week, but urged supporters to help get people signed up for care by mail, phone, and in person as well.

Congressional aides say the strategy by Republicans in the House of Representatives is aimed at putting a more human aspect to opposition arguments that have been largely abstract up to now.

"Facing hardships as a result of Obamacare? We want to hear your story," said a message posted to the website of the House Energy and Commerce Committee, a panel led by Republican Representative Fred Upton, whose bill to allow insurers to renew canceled insurance policies won approval on Friday from House lawmakers, including 39 Democrats.

A similar bill, sponsored by six Democrats in the Democratic-controlled U.S. Senate, appeared to be on hold for the time being, thanks partly to Obama's decision last week to let people keep old health insurance policies for the time being.

That left Senate Republicans searching for other vehicles to put Senate Democrats on the spot over Obamacare, particularly members facing competitive re-election races in November 2014.

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Among the options being considered, according to a Senate Republican leadership aide, is attaching an Obamacare repeal measure to some other bill, ideally something Democrats support, such as a proposal to raise the minimum wage.

The problem-plagued rollout that began on October 1 has hurt the popularity of the healthcare initiative, but the decline has been fairly modest, a Reuters/Ipsos poll showed on Monday.

Forty-one percent of Americans expressed support for the healthcare law in a survey conducted from Thursday to Monday. That was down 3 percentage points from a Reuters/Ipsos survey taken from September 27 to October 1.

Opposition to the law stood at 59 percent in the latest poll, versus 56 percent in the previous survey.

"There has been some shift ... but the shift has been small," said Ipsos pollster Chris Jackson.

While Obama administration officials, including website project manager Henry Chao, said they were making steady progress in improving the website, the repairs cited by officials do not resolve some of the thorniest problems, including fixes needed to allow insurers, Web brokers and insurance agents to help meet the enrollment challenge.

Outside technical experts still believe the website is unlikely to function well under high volumes.

White House spokesman Jay Carney told reporters the government was also moving forward to develop "additional channels" for signing up, including "direct enrollment" through insurance companies.

"We reconfigured various system components to improve site responsiveness. This has increased performance across the site," Chao, deputy chief information officer at the Centers for Medicare and Medicaid Services, said in written testimony submitted to a House of Representatives oversight subcommittee.

(Additional reporting by Roberta Rampton, Richard Cowan and Jeff Mason in Washington and Curtis Skinner in New York; Editing by Fred Barbash, Grant McCool and Peter Cooney)