Democrats say no, that Reid's comments - while unfortunate - were nothing like Lott's.
Reid apologized to Obama and a handful of black political leaders after a new book reported that he was favorably impressed by Obama during the 2008 presidential campaign and, in a private conversation, described the Illinois senator as a "light-skinned" African-American "with no Negro dialect, unless he wanted to have one."
Obama, who tries to steer clear of the political thicket of race and politics, accepted the apology and said he wanted to close the book on the episode. Republicans were eager to keep it open Sunday, comparing Reid's remarks to those that cost Trent Lott the Senate leadership in 2002 and questioning why there was different reaction now.
Lott had cheered the 1948 presidential campaign of Strom Thurmond - a segregationist Democrat opposing President Harry Truman - during a 100th birthday tribute to Thurmond, by then a longtime Republican senator.
Lott, R-Miss., eventually apologized but resigned nearly two weeks later after a growing number of Republicans questioned his effectiveness, especially after he told Black Entertainment Television he supported affirmative action, no longer opposed the Martin Luther King Jr. holiday, and would back programs aimed at minorities. He resigned from the Senate in 2007.
In Reid's case, at least so far, Democrats have been content to chide the Nevada Democrat and cast his remarks as inappropriate and, as Obama said, "unfortunate."
"There is this standard where the Democrats feel that they can say these things and they can apologize when it comes from the mouths of their own," Republican Party Chairman Michael Steele, who is black, said Sunday. "But if it comes from anyone else, it's racism."
Sen. John Cornyn, R-Texas, the chairman of the National Republican Senatorial Committee, said in a statement that Reid should step down, calling his comments "embarrassing and racially insensitive."
"It's difficult to see this situation as anything other than a clear double standard on the part of Senate Democrats and others," Cornyn said.
Former Rep. Harold Ford, an African-American who is chairman of the Democratic Leadership Council, called Reid's remarks "an unusual set of words."
But in an interview Monday on NBC's "Today" show, Ford said "I don't believe in any way Harry Reid had any racial animus. I think there's an important distinction between he and Trent Lott."
Ford, who is considering challenging Sen. Kirsten Gillibrand, D-N.Y., in his party's primary this year, also said he thinks no Democrats have called for Reid's ouster because "I think he has a (civil rights) record you can point to."
For his part, Reid has no intention of stepping down as majority leader and is "absolutely running for reelection," his spokesman, Jim Manley, said.
"The Republicans are saying this because they know they can't beat Harry Reid," Manley said in an e-mail. "The only way to get him is to try to push him out. Sen. Reid stands by the president and will continue his life's work to improve people's lives."
Democratic Sen. Jack Reed of Rhode Island rejected comparisons to the Lott episode.
"I think that's a totally different context. Harry Reid made a misstatement," Reed said. "He owned up to it. He apologized. I think he is mortified by the statement he's made. And I don't think he should step down."
Rep. Barbara Lee, D-Calif., chairwoman of the Congressional Black Caucus, released a statement saying, "Senator Reid's record provides a stark contrast to actions of Republicans to block legislation that would benefit poor and minority communities - most recently reflected in Republican opposition to the health bill now under consideration."
In their book "Game Change," Time magazine's Mark Halperin and New York magazine's John Heilemann report that Reid "was wowed by Obama's oratorical gifts and believed that the country was ready to embrace a black presidential candidate, especially one such as Obama - a 'light-skinned' African American 'with no Negro dialect, unless he wanted to have one,' as he later put it privately."
Steele appeared on "Fox News Sunday" and NBC's "Meet the Press." Reed spoke on the Fox program.