Senate Judiciary Committee members peppered Kagan with a wide range of questions, trying to discern a judicial philosophy and sense her temperament.
Democrats, who control 58 of the Senate's 100 seats, routinely praised the record of the 50-year-old solicitor general, as well as her poised performance this week, and predicted confirmation.
Many, though not all, Republicans vowed to keep firing away at her record and philosophy. President Obama nominated her to replace retiring Justice John Paul Stevens. The hearings were to continue Wednesday.
Kagan looked comfortable most of the time Tuesday, as if she were among old friends, but there were times when she sat alert and even turned combative as Republicans hammered away at issues such as restrictions on military recruiting at Harvard Law School while she served as its dean.
"I feel like she was not rigorously accurate in describing the whole nature of the circumstance, and so I'm disappointed in it," said Sen. Jeff Sessions of Alabama, the committee's senior Republican member.
Sessions said he emerged from the heated back-and-forth with Kagan on the issue more "troubled" about her nomination than before.
Still, she soldiered through her second day of testimony on Capitol Hill apparently in good shape to win Senate approval - barring a major gaffe - in time to take her seat before the court opens a new term in October.
Lawmakers from both parties asked Kagan, in sometimes scattershot fashion, about the day's biggest controversies, including abortion rights, campaign-finance laws, national security, and gun control.
Kagan's responses were similar to those of Supreme Court nominees past. But unlike her predecessors, Kagan wrote a 1995 article calling for judicial nominees to be more forthcoming.
On Tuesday, minutes into her testimony, she backpedaled, saying she now believed it would be inappropriate even to answer questions that might "provide some kind of hints" about her views on matters of legal controversy.