State Treasurer Alexi Giannoulias (D) holds a strong but not insurmountable lead in next week’s Democratic Senate primary in Illinois, according to a recent poll sponsored by the Chicago Tribune. Giannoulias led the Democratic field with 34 percent, followed by former Chicago Urban League President Cheryle Robinson Jackson at 19 percent and former Chicago Inspector General David Hoffman at 16 percent. Other candidates barely registered on the poll, but 25 percent of Democratic voters said they were still undecided heading into the Feb. 2 primary. A similar Tribune poll from early December showed Hoffman with 10 percent, making him the Democrat with the largest gain in the survey in the past six weeks. The latest poll, taken Jan. 16-20, surveyed 601 likely Democratic voters and had a margin of error of 4 points. Rep. Mark Kirk (R-Ill.), who is widely considered to be the frontrunner for the GOP nomination, posted even stronger numbers than in the previous Tribune poll. Kirk led his chief primary competition, real estate developer Patrick Hughes, 47 percent to 8 percent, with 35 percent undecided. Kirk’s lead increased from December, when he had the support of 41 percent of survey respondents and every other Republican in the poll had 3 percent or less.