State officials and physicians hoping to lift the nation’s declining Covid-19 vaccination rate have often asked the White House for the same thing: smaller vaccine vials. So far, they’re not encouraged. The demand for smaller vials, holding just one or two doses, is a reflection of how quickly the nation’s inoculation campaign has shifted away from mass vaccination sites to chipping away at the holdouts, one by one. The thinking is that smaller vials would enable more primary care offices, pharmacies and mobile clinics to administer shots when they find a willing patient, without having to worry about whether they would risk wasting other doses in the vial while much of the world is still desperate for vaccines. But for months, those calls to the White House have gone unfulfilled, leaving some state officials with the impression that the Biden administration is missing out on a chance to recruit key emissaries for the vaccination effort at another inflection point for the nation’s battle against Covid-19. Infections are up in every state while the Delta variant, the most contagious virus strain yet, quickly spreads and drives up hospitalizations in communities with lower vaccination rates.