Hillary Clinton has emerged from the rocky launch of her second presidential bid with a firm grip on Democratic voters and leads over three potential Republican rivals, a Wall Street Journal/NBC News poll finds.

The survey, taken in the days after Mrs. Clinton held her first public rally earlier this month, showed the former secretary of state garnering broad support from voter groups most likely to determine the election, including Latinos and women under the age of 50.

The poll underscores Mrs. Clinton’s strength as a candidate, both among Democrats and key constituencies that could tip the balance in a general election. But the results also show a clear desire among Democratic voters for a rival to emerge and hint at potential cracks in her support.

“She starts with advantages among very important groups,” said Republican pollster Bill McInturff, who conducted the survey with Democrat Fred Yang. He called her standing among fellow Democrats “the strongest and most advantageous” he has seen for any candidate entering a primary since he began working in politics in 1980.

Despite the strength of her early support, polls last week from the first-in-the-nation primary state of New Hampshire showed Sen. Bernie Sanders of Vermont pulling closer. And Mrs. Clinton’s failed 2008 bid offers a dash of caution, as well.