As Trump and Clinton begin aiming their fire at eachother, some surveys released in the past week reflect a close race nationally and in several battleground states.

In New Hampshire, according to a WBUR/MassInc poll released Wednesday, Clinton is holding the slimmest of leads over Trump in the Granite State, 44 to 42 percent.

In Georgia, a poll released Sunday by the Atlanta Journal Constitution gives Democrats some reason to hope they might be able to expand the battleground in November. Clinton was only four points behind Trump in the survey, 41 to 45 percent.

“The poll gives new heft to claims by Georgia Democrats that they can turn the Peach State blue, or at least a shade of purple, for the first time since Bill Clinton’s 1992 victory,” the Journal Constitution reported.

Nationally, a NBC News/Survey Monkey poll released Monday found Clinton holding only a three-point lead over Trump, 48 to 45 percent. The same poll last week found Clinton with a 5 point lead.

The slight tightening of the national race in the NBC survey tracks with other polls that have also shown Trump closing the gap with Clinton since he became the GOP’s presumptive nominee two weeks ago, after the Indiana primary. Clinton still leads most national surveys, but by slimmer margins than she once did – at the beginning of last month, Clinton was more than 10 points ahead of Trump in the RealClearPolitics average of national general election polls. Today, she’s only 5.2 points ahead.