Continued from page 1

While the president’s favorability ratings and those of Vice President Joseph R. Biden slipped considerably over their first three years in office, Mrs. Obama’s have remained strong.

Mr. Obama’s favorability rating now stands at 51 percent; Mr. Biden’s at 38 percent. By contrast, 66 percent of Americans have a favorable opinion of the first lady, about even with her ratings on Inauguration Day, according to the Pew Research Center.

That’s about where Laura Bush stood in the fourth year of her husband’s first term, and it’s considerably higher than Hillary Rodham Clinton’s 42 percent at the start of her husband’s fourth year as president.

Mrs. Obama is particularly popular with women and younger Americans, polling shows. And she does well with the moderate and liberal Republicans and independents whom Democrats will try to lure away in the fall elections.

So far, Mrs. Obama has headlined 32 fundraisers over the past 10 months, including six this year. Tickets to her political events range from $100 to $10,000, making them more accessible than higher-dollar fundraisers for the president. And her political schedule includes smaller cities, such as Charlottesville, Va., and Cape Elizabeth, Maine, that aren’t likely to draw a presidential visit.