But unlike Hillary Rodham Clinton, who as first lady crisscrossed the country for Democrats in 1998, visiting about 20 states, Mrs. Obama will keep to a fairly limited path. In a measure of how deeply unpopular her husband is in Republican-leaning battleground states, Democratic Senate candidates there worry that Mrs. Obama’s presence would tie them too closely to the president they are trying to distance themselves from, just as undecided voters are making up their minds.

“She’s awesome, but it just brings in the name Obama,” said a Democratic strategist in a state with a close Senate race, who, like most other Democrats interviewed, declined to be identified discussing politics involving Mrs. Obama…

Besides Ms. Nunn and Mr. Udall, just two other Senate candidates so far are expected to get visits from Mrs. Obama: Representative Gary Peters of Michigan and Representative Bruce Braley of Iowa. Mrs. Obama has recorded radio ads for Senator Jeff Merkley of Oregon and Mr. Peters.