Might Bibi's Government Fall Now? Yes - But Not So Fast
Procedural rules mean that early elections are unlikely before the Knesset fall session.

The dramatic resignation of United Torah Judaism and Agudat Israel from the government tonight (Monday) creates the specter of a coalition crisis and early elections for Prime Minister Netanyahu.
But Netanyahu actually has more time to solve the draft law problem than we think. There is no evidence that the Haredi parties wish to put forth their own no confidence vote to bring down the government, and so far some have even made a show of only resigning from coalition positions rather than the coalition, entirely.
The Prime Minister therefore probably has until the fall session of the Knesset t try and find some way to bring about a compromise everyone can live with on the draft.