If approved, Kennedy will control a $1.7 trillion agency that oversees food and hospital inspections, hundreds of health clinics, vaccine recommendations and health insurance for roughly half the country.

Mr. Kennedy appears to have most Republicans behind him as he seeks the job of health secretary, though he couldn’t escape his past stances on vaccines and abortion.

Robert F. Kennedy Jr. was confronted with a number of his baseless claims and a vexing abortion issue. But Republican senators treaded lightly.

Robert F. Kennedy Jr. faced aggressive questions about his skepticism of vaccines and other issues during the first of two scheduled Senate confirmation hearings.

WASHINGTON — Robert F. Kennedy Jr.’s anti-vaccine advocacy is outside the mainstream. His previous statements on abortion could alienate Republicans. But a new poll finds that not all of his controversial health goals are unpopular — in fact, at least one has broad support among Democrats and Republicans.

Robert F. Kennedy Jr. is seeking the support of the Republican-controlled Senate in his bid to become the nation’s top health official.