If an airline makes a substantial change like this they are obliged to offer you a full and unconditional refund Unfortunately airlines want to keep your money, so they often neglect to tell you this. Also it may not help you much if all the alternative flights are full or only have expensive tickets. But that's the way it is.
A good negotiating strategy is to call the airline, make it clear that the new times don't work for you and unless they can find something better you will be asking for a refund. Maybe then can reduce the price on the new flights (enough for you to be able to afford an overnight hotel). Or maybe they can take you off the first leg and give you a refund for that, so that you can book your own substitute first leg with another airline. They have an incentive to accept these arrangements because otherwise they will lose all your money. It will of course have helped of you have researched some alternatives in advance. And of course if you can find an alternative flight that works for you then just take the refund.