Final answer:
Congressional moderates supported the radical program through an appeal to unity and the preservation of the Union, embodied in the Omnibus Bill. However, not all radical legislative efforts succeeded due to significant opposition from various entities.
Step-by-step explanation:
The support of congressional moderates for the radical program was often won through various means, including the appeal to a larger shared goal of preserving the Union, as exemplified in Daniel Webster's speech for compromise. This sentiment aligned with those who supported Clay's scheme and the combined proposals into the Omnibus Bill. Unfortunately, the desire to preserve the Union did not always successfully outweigh sectional interests, and certain radical legislative attempts, such as national healthcare, were defeated due to strong opposition from organizations like the American Medical Association and conservative elements within Congress.