Bakiev has proposed reinstating acting Prime Minister Feliks Kulov, who resigned in December.
Only 25 deputies in the 75-seat parliament voted in favor of Kulov's candidacy today, RFE/RL's Kyrgyz Service reported.
Representatives of the presidential administration are due to meet with lawmakers on January 26 to try to resolve the deadlock.
Questions remain about what will happen if Bakiev nominates Kulov a third time with some government officials commenting that if parliament rejects Kulov a third time the president has the right to dissolve parliament.
Some lawmakers dispute that, saying the new constitution contains no such provision.
There were two small demonstrations outside parliament today. Some 100 people rallied in favor of Kulov and about 20 against his candidacy.