LANSING, MI - The race between President Barack Obama and challenger Mitt Romney for Michigan's 16 electoral votes remains close, according to a newly released poll that also shows the Republican having shored up his base in recent months.

Obama has more support, 44.2 percent to 40.5 percent for Romney in the poll of 600 likely voters commissioned by Grand Rapids-based public relations firm Lambert, Edwards & Associates, which also has offices in Lansing and Detroit. But the Michigan native is within the margin of sampling error of 4 percentage points, meaning they statistically are locked in a tight race.

More than 13 percent of respondents were undecided.

The poll provided to MLive was conducted by Denno Research on Oct. 9-10, before the vice presidential debate and Tuesday night's second presidential debate. The East Lansing polling company is run by Dennis Denno, chief of staff for a Democratic state senator.

Related: Compare the candidates, check out local races using our Voter Guide at MLive.com/VoterGuide.

Since the pollster's last survey in June - which had Obama and Romney tied at 40 percent each - Romney has closed much of the enthusiasm gap that existed between supporters of Obama and himself after the GOP primaries.

Forty-four percent of Republican respondents said they were very excited to vote for Romney, as opposed to 16 percent in June. Forty-eight percent of Democrats reported being very excited to vote for Obama, up from nearly 39 percent.

"More voters appear to have made up their minds, but the remaining weeks before Nov. 6 still offer opportunities for Obama and Romney to make their case and possibly persuade voters to switch sides," said Jeff Lambert, president and managing partner of Lambert Edwards. "Michigan is getting attention from both campaigns and will play an important role in deciding the ultimate winner."

It seems unlikely for now, however, that Romney will make a full-fledged attempt at Michigan, his native state and one which a GOP presidential candidate has not won since 1988. Politico on Tuesday quoted an unnamed senior Romney adviser saying the campaign does not intend to "blow smoke" about flipping big, Democratic-leaning battleground states such as Michigan.

The Super PAC supporting Romney is running TV ads in Michigan.

"What's most important for Mitt Romney is that he's strengthening his position within his own base," Denno said. "With the race this close, turnout is crucial."

Among voters identifying themselves as independents, Romney had 38.5 percent to Obama's 29.8 percent, with 26.6 percent unsure.

Romney was up among men overall, 43.3 percent to 40.7 percent, but trailed Obama among women, 47 percent to 38.2 percent.

Email David Eggert at deggert1@mlive.com and follow him on Twitter @DavidEggert00