Maryland Democratic gubernatorial hopefuls Anthony G. Brown and Douglas F. Gansler both opened campaign offices in their respective home counties Sunday, seeking to build enthusiasm among some of their core supporters.

Brown, the state’s lieutenant governor, told a crowd in Mitchellville that he was “excited, just like you” to see the results of a new poll Sunday in the Baltimore Sun showing him with a sizable lead over his rivals. But Brown, a former Prince George’s County delegate, cautioned that his campaign has a lot of work left to do in a primary still four months off.

“Don’t let those polls slow us down,” Brown said, comparing his campaign to a race car that needs to stay in high gear to climb a hill. His campaign also opened a new office in Howard County on Sunday.

The Sun’s poll showed that 35 percent of likely Democratic voters support Brown, while 14 percent support Gansler and 10 percent back Del. Heather R. Mizeur (D-Montgomery). About 40 percent of voters are undecided, however, according to the survey conducted for the Sun by OpinionWorks, an Annapolis-based firm.

Gansler, the state’s attorney general, made no mention of the poll during an appearance in Rockville, where he told an enthusiastic crowd that he feels good about where the campaign stands.

“Obviously, we have a lot of momentum going in this race, and we’re excited about it,” said Gansler, a former Montgomery County state’s attorney. “We know we’re going to win this.”

Gansler also used the event to announce the support of the Montgomery County Career Fire Fighters. The statewide chapter of the union previously endorsed Brown.

During his remarks, Brown highlighted one major difference with Gansler: Gansler’s support for a reduction in the corporate income tax rate from 8.25 percent to 6 percent.

Brown said that was a bad idea, saying the loss in revenue would threaten some priorities in coming years, including an expansion of pre-kindergarten education.

Gansler has argued that the reduction — to the same level as Virginia — would give Maryland a better shot and recruiting and retaining businesses and increase the state’s tax base.

Mizeur has also panned the idea, proposing instead to offer targeted tax rebates to small businesses.