The Supreme Court is expected to release its decision on the constitutionality of the law by June.
In April, roughly one in three Americans expressed confidence in the court — up from one in four in March, before oral arguments on the healthcare law took place.
The change was largely driven by an increase in trust among Republicans, 43 percent of whom expressed confidence in the court in April compared to 24 percent who did so in March.
This jump could stem from perceptions that the court's conservatives were tough on the law, which remains highly unpopular with Republicans, during arguments.
The poll also found that many minds have changed over which factors will influence the justices in their decisions.
In March, one in the three (33 percent) said their views — liberal or conservative — would decide their votes, while in April, a slightly higher number (39 percent) said their "analysis and interpretation" of the law would rule the day.
Only 6 percent in both cases thought the view of average Americans would influence the justices' opinions.
The high court held arguments over a rare three-day period that dominated political media coverage nationwide.
In spite of fierce reactions on both sides of the debate, the public's opinion on the law's components barely shifted in response.
Americans, for example, remain split in their general opinion on the law, with 42 percent in favor and 43 against in April, compared with 41 percent in favor and 40 against in March.
And a whopping seven in 10 were against the individual mandate to buy health insurance, with three in in favor — mirroring figures from March.
The poll was conducted April 4-10 as part of a month-to-month tracking project by the Kaiser Family Foundation. It surveyed 1,210 adults and has a margin of error of 3 percentage points.