General Assembly members attended a briefing Wednesday on the financial challenges of the state employee health insurance plan.

They learned the Legislature may have to find another $1 billion over the next two years to meet the claims of the plan’s 667,000 members. State employees and retirees also may have to pay more in the form of 31 percent premium increases over the same period or in reduced coverage.

The amounts don’t include an additional $300 million needed by this spring because the plan is in danger of running out of money.

Lawmakers on Tuesday heard about the state’s broader budget problems.