The decision Friday by three Democratic senators to vote for a Republican budget sent shockwaves through the state’s political system and left the next two-year spending plan in limbo. State Sens. Gayle Slossberg, D-Milford, Paul Doyle, D-Wethersfield, and Joan Hartley, D-Waterbury, declined to vote for a $41.4 billion Democrat-backed budget and instead allowed a Republican version to clear the state Senate by a 21-15 vote.