“The failure to ratify by state employees does more harm to them and the cause of labor than anything their enemies could possibly achieve,” Donald E. Williams Jr., a Democrat who is president pro tem of the State Senate, wrote colleagues in a message announcing the special session. “It’s unbelievable that they don’t understand that.”

But the rejection reflected a complicated whirl of factors, not least of them the approval process itself, in which about 60 percent of workers voted in favor of the agreement only to have it fail.

Under longstanding collective bargaining rules, the agreement needed to be approved by 14 of the 15 unions in the State Employees Bargaining Agent Coalition, with the bargaining units voting in favor representing 80 percent of the 45,000 state workers covered by the deal.

What doomed the package was its rejection by two unions — including, notably, the American Federation of State, County and Municipal Employees Council 4, which covers about one-third of all unionized state employees.

The opposition centered on suspicions about the health care provisions, particularly fears that the deal would eventually place employees in a new state insurance program, called SustiNet. Union and state officials said health care could not be changed again without employee approval until 2022.

It also reflected the beliefs among some members that they could win a better package if they rejected this one and that the layoff threats were more posturing than reality. Mr. Malloy has insisted that there will be no renegotiation and that large-scale layoffs will be swift and certain.

The process reflected the information blizzard of the new media age, with union officials saying misinformation spread by right-wing groups, particularly the Yankee Institute for Public Policy, a conservative research organization, helped to torpedo the agreement. The institute called the claim of meddling “delusional.”