The final health-care legislation that House Democrats are striving to pass this weekend would give about 19 million Americans subsidies averaging $6,000 to help pay premiums and other insurance charges, an unprecedented government investment in private health policies that leaves lingering questions about whether coverage would truly become affordable.

The details of the subsidies, which emerged in the past day, provide the clearest picture yet on a central question that has hovered over the health-care debate since it began a year ago: How much help would the government give people to cope with the expense of medical insurance?

In the final version Democrats produced, the subsidies would be part of a two-prong approach by the government to extend coverage to the vast...