“It left a bitter taste in my mouth,” Councilman Hickey said.

He says he will vote against the budget on Monday night if the two positions aren’t kept in the spending plan. The budget session begins at 6:30 p.m.

At Monday’s final budget session, council members will also consider giving themselves $4,000 pay raises, among dozens of other budget modifications they will be asked to take action on.

Last week, Councilman Cliff G. Olney III was the only one who opposed cutting two of the five police officer positions from the budget.

Since Tuesday’s meeting, Councilman Hickey has discussed the issue with councilors Olney and Lisa A. Ruggiero, who also is reconsidering her initial support to remove them from the budget.

Councilwoman Sarah V. Compo Pierce, who couldn’t be reached for comment, is also considering retaining them in the budget, he said.

In his proposed budget, City Manager Kenneth A. Mix proposed adding 24 new positions at a cost of $1.4 million, saying that they would be covered by an unexpected increase in sales tax revenues.

At last Tuesday’s meeting, council members decided to reduce that number by four — two police officers and one position each in the public works department and codes office.

During earlier budget deliberations, Police Chief Charles P. Donoghue told council…