First Read is a morning briefing from Meet the Press and the NBC Political Unit on the day's most important political stories and why they matter.

Trump closes the battleground gap, but is still unable to overtake Clinton

Yesterday brought us a whopping 10 battleground state polls, and four more NBC/WSJ/Marist polls (!!!) are set to be released first thing tomorrow morning. The good news for Donald Trump? He’s narrowed the gap: Ohio is tied; Florida is no longer trending in Hillary Clinton’s direction; and this all makes it much harder for rebellious GOP delegates to dump Trump at the convention.

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But here’s the bad news for him: These polls -- which mostly show Clinton either ahead or tied in these battlegrounds -- were all taken during or after Clinton’s roughest week of the general election, with FBI Director James Comey’s rebuke over her emails. So you could view these battleground numbers as a floor for Clinton, while Trump is still unable to break 40% in many of these states. (Indeed, look at the high undecided numbers; voters moved away from Clinton, but they didn’t move toward Trump.) And what should ring alarm bells for the GOP is the polling in Colorado and Virginia, where Clinton is up in high single digits/double digits.

On the other hand, these polls also come as Team Clinton has been outspending Team Trump over the battleground airwaves by a 40-to-1 margin. So it’s possible that Trump could improve his numbers if/when he starts airing TV ads. But here’s the bottom line: The email story alone isn’t going to win the presidential race for Trump. He’s got to deliver on his VP pick and convention to overtake Clinton. Here are yesterday’s polls:

Colorado: Clinton 48%, Trump 35% (Monmouth); Clinton 44%, Trump 34% (Fox)

Florida: Trump 42%, Clinton 39% (Quinnipiac)

Iowa: Clinton 42%, Trump 39% (NBC/WSJ/Marist)

Ohio: Clinton 39%, Trump 39% (NBC/WSJ/Marist); Clinton 41%, Trump 41% (Quinnipiac)

Pennsylvania: Clinton 45%, Trump 36% (NBC/WSJ/Marist); Trump 43%, Clinton 41% (Quinnipiac)

Virginia: Clinton 44%, Trump 37% (Fox)

Wisconsin: Clinton 43%, Trump 37% (Marquette Law)

Looking at the gender, racial, geographical, and education gaps

Our three NBC/WSJ/Marist polls of Iowa, Ohio, and Pennsylvania also reveal the familiar gaps we’ve seen so far in this Clinton-vs.-Trump race.

The gender gap

Iowa: Men: Trump 48%, Clinton 33%; Women: Clinton 49%, Trump 31%

Ohio: Men: Trump 47%, Clinton 32%; Women: Clinton 47%, Trump 31%

Pennsylvania: Men: Trump 42%, Clinton 41%; Women: Clinton 49%, Trump 30%

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The racial gap

Ohio: Whites: Trump 43%, Clinton 33%; African Americans: Clinton 88%, Trump 0%

Pennsylvania: Whites: Clinton 40%, Trump 40%; African Americans: Clinton 91%, Trump 0%

The geographical gap

Iowa: Des Moines area: Clinton 52%, Trump 31%; West: Trump 53%, Clinton 27%

Ohio: Cleveland: Clinton 54%, Trump 30%; Columbus area: Clinton 44%, Trump 33%; Ohio Valley and West: Trump 47%, Clinton 29%

Pennsylvania: Philadelphia: Clinton 74%, Trump 12%; Philly suburbs: Clinton 55%, Trump 26%; Central: Trump 44%, Clinton 39%; West: Trump 43%, Clinton 38%

The education gap

Iowa: White college grads: Clinton 44%, Trump 37%; White non-college grads: Trump 43%, Clinton 37%

Ohio: White college grads: Clinton 39%, Trump 34%; White non-college grads: Trump 49%, Clinton 30%

Pennsylvania: White college grads: Clinton 47%, Trump 37%; White non-college grads: Trump 43, Clinton 33%

Still, the email story has damaged Clinton

While Trump has been unable (for the most part) to overtake Clinton in these battleground polls, there’s no doubt that the last week did some serious damage to the presumptive Democratic nominee. “Hillary Clinton has emerged from the F.B.I. investigation into her email practices as secretary of state a wounded candidate with a large and growing majority of voters saying she cannot be trusted, according to the latest New York Times/CBS News poll,” per the New York Times. “As Mrs. Clinton prepares to accept the Democratic Party’s nomination at the convention in Philadelphia this month, she will confront an electorate in which 67 percent of voters say she is not honest and trustworthy. That number is up five percentage points from a CBS News poll conducted last month, before the F.B.I. released its findings.”

Trump to make VP pick official on Friday

Donald Trump tweeted last night he will announce his choice for running mate at 11 a.m. Friday in Manhattan. “Sources previously told NBC News Trump would announce his choice for vice presidential candidate Friday. Indiana Gov. Mike Pence, New Jersey Gov. Chris Christie, and former House Speaker Newt Gingrich have been mentioned as finalists,” NBC writes. It increasingly appears as if the VP race is coming down between Gingrich and Pence -- a conventional Republican pick (Pence) vs. a disrupter (Gingrich); someone with a political future (Pence) vs. someone with nothing left to lose (Gingrich).

GOP convention speaking list: showcasing Trump’s family and friends, not showcasing the party as much

Our immediate takeaway from the partial list of speakers for next week’s GOP convention is that it’s about 50% Trump family and friends, versus 50% party officials and elected. Usually, it’s 90% party, 10% friends and family. Oh, and campaign officials tell NBC’s Hallie Jackson that Tim Tebow WILL speak at the convention, even though he isn’t on this initial list.

Five stories to watch at today’s Republican Convention Rules Committee meeting

Another storyline we’re watching today is the showdown in Cleveland, beginning at 8:00 am ET, as opponents push for changes to make it more difficult for Trump to win the necessary majority of delegates to claim the nomination. Here’s NBC’s Alex Jaffe and Leigh Ann Caldwell on the five things to watch, and here’s NBC’s Leigh Ann Caldwell on the woman who’s leading the charge to change the rules against Trump.

Clinton hits Trump in new TV ad

As for Hillary Clinton, her campaign is up with a new TV ad hitting Trump. It shows children watching some of Trump’s most controversial statements. “Our children are watching,” the ad states. “What example will we set for them?”

Veepstakes Watch

Don’t miss the latest installment of VP Watch… Gingrich and Christie are on the initial convention speakers’ list, but Mike Pence is not… Gingrich said on FOX last night that Trump is “like a pirate”… Trump indicated “I probably am thinking about two” choices… POLITICO Magazine offers “The Millennial’s Guide to Newt Gingrich”… Alex Seitz-Wald writes on how Republicans will take aim at Clinton’s VP pick… Tim Kaine campaigns with Clinton today in Virginia… And Reuters looks at the pros and cons of Kaine being the “safe” pick…

On the trail

Hillary Clinton addresses the League of United Latin American Citizens conference in DC at noon ET, then meets with Senate Democrats on Capitol Hill around 1:00 pm ET, and then campaigns with Tim Kaine in Annandale, VA at 3:15 pm ET. Don’t forget to check out the political unit’s rolling minute-to-minute coverage of all the latest 2016 developments at the On the Trail liveblog at NBCNews.com.

Countdown to GOP convention: 4 days

Countdown to Dem convention: 11 days