That is a tall order. Mr Kumar and his Janata Dal(United) are firm that they cannot accept Gujarat chief minister Narendra Modi as the prime ministerial nominee for the coalition fronted by the BJP, the National Democratic Alliance or NDA.
Mr Kumar's party has indicated that this weekend, it may formally ask the BJP soon to come clean on its plans for Mr Modi. Senior JD(U) leaders are meeting in Delhi at a national executive meeting.
Outside the meeting venue, there are massive posters of the two JD(U) powerhouses, Nitish Kumar and Sharad Yadav, taking on Sonia Gandhi and Manmohan Singh with the heading - "2nd Mahabarath War 2014." No BJP leader can be seen in any of the posters.
"We cannot set a deadline for the BJP. But we cannot wait indefinitely," JD(U)'s Ali Anwar told NDTV today.
BJP chief Rajnath Singh, who will meet with Mr Kumar and the other JD(U) powerhouse Sharad Yadav this evening, will try to broker a deal.
The fact that Mr Modi was in charge of Gujarat when hundreds of Muslims were killed in communal violence in 2002 makes him an unacceptable national-level leader for Mr Kumar, who relies on the 15 percent Muslim population in Bihar for electoral support.
But even Mr Modi's detractors within the BJP-and there are some powerful ones-have been forced to concede his strength as a vote-getter. Since his third re-election in December as Chief Minister of Gujarat, the BJP cadres have been pushing their leaders to announce Mr Modi as the presumptive Prime Minister.