Despite a significant split-off from his own Syriza party, he was able to gain enough votes that he could form a new coalition with his previous small partner party Anel (Independent Greeks). Anel is typically described as a rightwing populist party. But their basic economic program, an end to austerity but keeping Greece in the eurozone, is compatible with Syriza's.
The new government has a narrower majority than his previous one. But at the moment, Tsipras is backing the latest brutal Troika program forced onto his last government, so he will get solid support for other non-coalition parties on votes in accord with the Troika's directions. Which means, above all, the directions from the Compassionate Pastor's Daughter Angela Merkel.
Former Finance Minister Yanis Varoufakis comments on the challenges for Tsipras in The lenders are the real winners in Greece – Alexis Tsipras has been set up to fail The Guardian 09/23/2015:
The third promise is key to Tsipras’s success. Having accepted a new extend-and-pretend loan that limits the government’s capacity to reduce austerity and look after the weak, the surviving raison d’être of a leftwing administration is to tackle noxious vested interests. However, the troika is the oligarchs’ best friend, and vice versa. During the first six months of 2015, when we were challenging the troika’s monopoly over policy-making powers in Greece, its greatest domestic supporters were the oligarch-owned media and their political agents. The same people and interests who have now embraced Tsipras. Can he turn against them? I think he wants to, but the troika has already disabled his main weapons (for example by forcing the disbandment of the economic crime fighting unit, SDOE).Varoufakis has not aligned himself with the dissenting split from Syriza. But he declined to stand for his parliamentary seat in last Sunday's election because of his disagreement with Tsipras' acceptance of the Compassionate Pastor's Daughter's brutal austerity program.
In 2014 the conservative prime minister Antonis Samaras found himself in a similar conundrum, having to implement a failed troika programme. He resorted to feigning allegiance to the troika while stonewalling and petitioning it for laxity, lest Syriza win.
Will Tsipras have more success in faking commitment to another failed troika programme? The prospects are not bright, but we should not write him off. His fate depends on whether his new government remains connected to the victims of its troika agreement, implements genuine reforms to give bona fide business some confidence to invest, and uses the intensification of the crisis to demand real concessions from Brussels. It is a tall order. But then victory, however sweet, is not the point. The point is to make a difference.