Sen. Lamar Alexander (R-Tenn.) is challenging President Obama's promise that if Americans like their current health care plan, they could keep it under the new health care law.

The president has made that promise since 2009, but now he's "tweaking" his pledge, after millions of Americans received cancellation notices from their insurance companies.

Alexander said during a Senate committee hearing Tuesday that the promise is still prominent on the White House's website.

"The president has said repeatedly - and I looked up the White House website this morning - 'If you like you plan then you can keep it, and you don't have to change a thing under the health care law.' Let me repeat, 'You don't have to change a thing due to the health care law.' That's the White House website today," said Alexander.

The Tennessee senator told the Senate committee that there's more bad news.

"For millions of others, employers are dropping insurance programs as they discover the added costs of Obamacare," Alexander said Tuesday. "For these Americans, the new promise is if you want health care, go find it on a website the administration says won't be working properly until the end of November. That's an unwelcome Christmas present."

The president maintains even though some people are getting kicked off their existing plans, virtually every insurer is quote "offering new and better plans."

Marilyn Tavenner, the administrator for the Centers for Medicare and Medicaid Services, testified in the committee today. She said the site is still improving.