With slightly more than a month until Election Day, the push is on for the presidential candidates to lock up battleground states. Both Democrat Hillary Clinton and Republican Donald Trump have campaigned hard in North Carolina, which could prove a crucial swing state come Nov. 8. 

First lady Michelle Obama, a Clinton surrogate, spoke Tuesday in the state to support the Democratic candidate. Obama even threw a little shade at Trump's complaints over a faulty microphone at the first debate, which polls showed the GOP nominee lost.

"Hillary is tough, when she gets knocked down she doesn't complain, she doesn't cry foul," Obama said, tapping the microphone at her lectern. "No she gets right back up."

The latest surveys show Clinton holds a narrow lead in North Carolina over Trump. The Real Clear Politics average of polls give her a 1.3 percentage point edge over the GOP nominee in a three-way race. Clinton leads in all the recent polls, but the margin varies widely.

A Bloomberg poll of likely voters that talked with voters Thursday through Sunday had the closest race, Clinton garnering 46 percent support to Trump's 45 percent. A WRAL poll of likely voters gave her a two-point edge, 46 percent to 44, while a Quinnipiac survey gave her a 3-point lead. A poll from Elon University had Clinton the furthest ahead, finding she was up by nearly 6 percentage points. All of these surveys were performed after the first presidential debate in September and most found, to varying extents, that Clinton had seemingly seen a bump in support after winning the matchup against Trump.

Nate Silver, editor of the data-driven website FiveThirtyEight, published an article Tuesday that said North Carolina was "becoming a backstop for Clinton." It's a crucial state, especially because of the its demographics, and it could act "as a potential hedge for Clinton in the event of a collapse in her support among white voters without college degrees, especially in the Midwest." So, in theory, North Carolina could save Clinton should she lose states like Ohio and Michigan. 

Early Wednesday morning, FiveThirtyEight's polls-only election forecast gave Clinton a 58 percent chance of winning North Carolina and a 75 percent chance of winning the election.