Her broad appeal among Democratic voters has prevented liberal complaints against the party’s Wall Street faction from mushrooming into an electoral insurgency. Her star power — and the potential for a ceiling-breaking White House victory — has helped obscure a vexing reality for the post-Obama Democratic Party: As much as it advertises itself as the party of a rising generation, the Democrats’ farm team is severely understaffed, and many of its leading lights are eligible for Social Security.

Jerry Brown, perhaps the most successful big-state Democratic governor in the country, is 76. (He ran for president two decades ago — as the anti-Clinton candidate.) The top four congressional Democrats are all 70 or older. And as Democrats look for new recruits to run in 2016, there are fewer up-and-comers, and more prospects older than 60 looking to make up for losses in previous elections, including Joe Sestak of Pennsylvania, Russ Feingold of Wisconsin and Ted Strickland of Ohio, who are all eying Senate seats.

“When people bring up the presidential race to me, they bring up Secretary Clinton,” said Jason Kander, 33, Missouri’s secretary of state and a Democrat running for the Senate. “I have just not had many conversations where people talk about different candidates.”

Down the ticket, the party’s problems are worse. The two midterm elections since President Obama’s 2008 victory have wiped out an entire generation of Democratic state officeholders, costing the Democrats more than 900 state legislative seats and 11 governorships, according to an internal Democratic National Committee assessment released last month.

Republicans have been more aggressive in steering donors to less glamorous state races, electing governors and legislative majorities whose sweeping rollback of union rights has further damaged Democrats in states in which they are already reeling.

“The other side has killed us at that stuff,” said Steve Rosenthal, a Democratic strategist.

The shift has provided Republicans an advantage in redistricting and fund-raising: In 10 top presidential swing states, according to data collected by the National Institute on Money in State Politics, Republican state parties raised $350 million over the last four years, compared with $215 million for Democratic state parties.

“Obviously, Florida’s struggled at the state level for Democrats,” said Mark S. Pafford, the Democratic leader in the state’s House of Representatives, where Democrats now hold just over a third of the seats. His hope, Mr. Pafford said, is that a candidate of Mrs. Clinton’s stature “reinvigorates the base to go out and find motivation in Democratic leadership.”