LYNN – City councilors and a new councilor-elect barely have time to catch their breath after winning election night victories before they decide a two-way – potentially three-way – contest for City Council president.Councilor at large Daniel Cahill and Ward 2 Councilor William Trahant Jr. sought commitments from colleagues and locked up votes in support of their presidencies even as they worked to get reelected Tuesday night.”I want to be council president because I want everyone to have an equal seat at the table. If I disagree with other councilors, even the mayor, I want them to be heard,” Cahill said.Trahant said his knowledge of city government and the city gives him the skills to be council president. He said he has “handshakes” from four potential supporters “and I’m talking to a couple other people.”They need six out of 11 council votes to win the presidency.Council President Timothy Phelan’s council term and presidency runs through year’s end following his defeat in Tuesday’s mayoral election. Phelan has held the presidency since 2006.Top election night vote-getter Gordon “Buzzy” Barton, and self-acknowledged Cahill ally and Councilor at large-elect Brendan Crighton pledged their votes Wednesday to Cahill. Ward 7 Councilor Rick Ford said Trahant has solicited his vote and Ward 3 Councilor Darren Cyr, a Trahant ally, declined to identify the presidential candidate who solicited his vote.”I love Billy; he’s old-school like me; but I’m not doing any handshaking yet,” Ford said.For now, at least, Cahill and Trahant are not going to secure Ward 1 Councilor Wayne Lozzi’s vote.”I’m interested in being council president,” Lozzi said.No matter whom they support, councilors said they want Phelan’s successor to strengthen relations with Mayor Judith Flanagan Kennedy and “move forward” on agendas encompassing citywide improvements.”I want to see things moving forward. Dan has a better relationship with the mayor,” Barton said.The council president presides over council meetings and shapes agendas for the council’s twice-monthly meetings. The city charter calls for council office elections to take place on the first Monday in January, but former Council President James Cowdell said a presidential hopeful is likely to secure votes needed to win election sooner rather than later.Cowdell said councilors – including Ward 5 Councilor-elect Dianna Chakoutis – face “a lot of pressure” from presidential hopefuls seeking votes.”Dan and Billy are liked by all – it’s not an easy choice, and you don’t want to make the wrong choice,” Cowdell said.Kennedy was a councilor at large in 1997 when Cowdell and former Councilor at large Salvatore Migliaccio competed for the presidency. She teamed up with former Ward 1 Councilor Jane Teal, and the two women sat down with each presidential candidate and let the men make their pitch.”That’s how we decided who to support,” she said.Kennedy said her “inclination is to stay completely out” of the current presidential competition, but she said councilors have a big decision to make in picking Phelan’s successor.”The decision ultimately will indicate if the council is interested in going in a new direction or the same direction it has for 10 years. I think there is going to be a very clear difference between the candidates,” she said.Councilor at large Hong Net could not be reached for comment Wednesday. Chakoutis and Councilors Richard Colucci and Peter Capano said presidential hopefuls have solicited their votes but said they have not decided who they will support.