We've seen a smattering of new polls of the nascent 2016 campaign in recent days.

The good news for Jeb Bush: Most of them show him as a front-runner.

The bad news: There's plenty of bad news.

Of the four major Iowa and New Hampshire polls released over the past 10 days, half show Bush leading, and all show him toward the front. This is a function, in large part, of name recognition. But there are plenty of warning signs, too.

Here's a quick recap:

1) His image numbers are not good

The lone Iowa poll in the bunch shows that likely Iowa GOP caucus-goers view Bush more negatively than anybody not named Chris Christie. Just 46 percent had a favorable opinion of Bush in the Bloomberg/Des Moines Register poll, while 43 percent had an unfavorable one. Again, this is Republicans.

Bush's numbers in New Hampshire (where the universe of voters is less conservative) were better, but not by a huge amount. He was at 61 percent favorable/26 percent unfavorable in the Bloomberg/Saint Anselm College poll released over the weekend, and at 47/33 in the University of New Hampshire/WMUR-TV released just prior.

Part of this is that Republicans today are just fussier when it comes to purity, and Bush can't help but be seen as the establishment (i.e. "moderate," to the tea party) candidate. But it's also clear they have some preconceived notions about Bush that he'll have to dispel.

Which brings us to...

2) The name isn't helping

Bloomberg asked likely New Hampshire primary voters whether they viewed Bush's and Hillary Rodham Clinton's prospects as being more tied to their own accomplishments or to their family name.

While just 21 percent of Democrats said Clinton is a front-runner because of her family connections, 59 percent of Republicans say the same about Bush. Only 31 percent said Bush is where he's at because of his "unique qualities and achievements."

Similarly, a Washington Post/ABC News poll released a few weeks ago showed the Bush name was a net-negative for 33 percent of voters, while just 11 percent said it was a reason to vote for him. It was more even among Republicans, but again, it wasn't nearly the benefit the Clinton name was.

3) The porridge question

The other reason Bush's numbers might suffer -- in addition to him being a Bush -- is that he's seen as too moderate. We're not sure how much people have actually processed his positions in favor of comprehensive immigration reform and Common Core, but already 37 percent of likely Iowa caucus-goers see him as "too moderate." Another 7 percent say he's "too conservative."

In fact, the 40 percent who say Bush is ideologically "about right" is lower than Ben Carson (49 percent), Ted Cruz (48), Mike Huckabee (57), Rand Paul (55), Rick Perry (62), Mitt Romney (46), Marco Rubio (53), Rick Santorum (49) and Scott Walker (56). That's pretty much anybody who is reasonably well-known (and isn't named Chris Christie).

4) Immigration and Common Core

While most likely New Hampshire primary voters don't yet say these issues are disqualifying, plenty still do. The Bloomberg poll showed 41 percent of likely New Hampshire primary voters say Bush's pro-comprehensive immigration reform position is a deal-killer, while 20 percent say the same of Common Core. Those are significant chunks of voters who say Bush's positions are non-starters.

Perhaps more illustrative, just 40 percent say Common Core is not a real problem for them when it comes to Bush, and just 22 percent say the same of his immigration position. The others are in the mushy middle (but haven't ruled out supporting him) or haven't decided.

The good news is that these liabilities, at this point, aren't yet overwhelming; Scott Walker's lack of foreign policy experience, for comparison, is deemed as a deal-killer by 28 percent of Republicans — something we have a hard time believing will pan out.

All of this, indeed, is quite preliminary. While Bush has been something of an open book, the campaign hasn't actually begun in earnest, and thus he hasn't had much of a chance to combat these early preconceived notions. These notions, in other words, probably aren't based on a whole heck of a lot.

What these numbers prove, though, is that there are preconceived notions that he'll have to contend with. And they're generally bigger hurdles than his opponents have to clear.

Of course, his opponents aren't likely to have the kind of funding Bush does, either.