(CNN) Former Rep. Michael Grimm is looking to get his old job back representing Staten Island after spending a stint in federal prison for tax evasion. He's is running in Tuesday's Republican primary in New York's 11th Congressional District against current Rep. Dan Donovan.

Grimm may just win the primary.

The polling for the race is limited. A Siena College poll taken a little less than a month ago had Grimm ahead of Donovan by 10 points. The only other poll released this month was conducted by a group that is owned by a consulting firm that has worked for Donovan. That poll, which does not meet CNN's standards, had Donovan leading by single digits.

Either way, Grimm has a fighting chance.

The question how can a convicted felon be in a position to win, and what does the outcome of the race mean for the fall campaign?

1. Grimm was good at constituent services

When I visited with Grimm this week, I asked him what the number one thing a national audience might not understand about his popularity. He responded, "how hard I worked and how effective I was as the congressman for four years ... I went about my constituent services in a very different way than I would say 95% of members of Congress. And that's personal touch. I show up personally when you have a problem."

His supporters agreed with that. Veronica Petersen, whom I met at a Superstorm Sandy survivors event, told me, "After Sandy and during Sandy, Michael Grimm was the man. I mean, he came in like ... Whoa. He helped us from day one. He was the one who got the flood insurance for us. It was 25% after Sandy. A lot of us couldn't afford that He went to Congress and got a bill that enacted it and brought it down to 18%. I mean, he does that for people."

Indeed, Grimm's efforts to pass Sandy legislation was an instance in which he voted for his district's interests and against his own party. The $51 billion aid package passed the House with only 49 Republicans voting for it compared to 179 against it.

2. Even with Trump's endorsement, Donovan is seen as not pro-Trump enough

Like in any Republican primary in 2018, President Donald Trump is at the top of the agenda. Those who are seen as for him are largely in better shape than those who are seen as not supporting his agenda.

Donovan has Trump's endorsement, which could end up saving him in the end.

But Donovan's voting record has given Grimm an attack line. Only 25 House Republicans in this Congress have voted with Trump less often. Donovan, for example, voted against the President's tax cut plan.

When I asked Grimm if there were issues on which he disagreed with the President, he couldn't "see really any issues that I would disagree with." Perhaps not surprisingly, 54% of likely primary voters said they thought that Grimm would work better with Trump in the Siena poll. Only 29% said they thought Donovan would work better with Trump.

It should be noted that when Grimm was in Congress, he wasn't a down-the-line Republican either. If you were to average his last two years in Congress, he voted with then-Democratic President Barack Obama 23% of the time. Only six Republicans out of 236 recorded by Congressional Quarterly voted with Obama more often during that span.

Being pro-Trump goes beyond just the numbers, however. Grimm has used the President as a type of blocker when it comes to the charges against him. Like the President and the Russian investigation, Grimm has said his conviction was part of a "witch hunt" by the Obama administration. He also said he won't release his taxes. Trump hasn't released his.

It's also about personality. Trump made a name for himself in the Republican primary by lobbing insults and being quick on his feet. Grimm fits that same mold. During a back-and-forth with Donovan during a recent debate, Grimm told Donovan, "Oh, I've already predicted your future. In fact, I'm going to define it when you get beat on June 26."

3. Grimm needs only hardcore supporters to win the primary

A victory by Grimm on Tuesday will say little about how the district at-large feels about him. Instead, it will be a sign that he had a group of hardcore supporters who were willing to turn out for a late June primary. To vote in a Republican primary in New York, you have to be a registered Republican. They only make up 27% of the voters in the district.

In 2016, only 33,022 votes were cast in the Republican primary for president. That, of course, was a marquee matchup. This is a congressional primary. The last time there was a competitive Republican primary for this seat was back in 2010. Back then, just 14,117 were cast in the primary.

Adding to the confusion is that New York is one of few states in the nation to have not one, but two state primaries. Traditionally, New York's primary has been in September, but a federal court ruling in 2012 mandated that federal primaries take place earlier than that so that servicemembers and those abroad had enough time to get their general election ballots and return them on-time. Primaries for state and local offices are still in September, while federal primaries are now in June.

The amount of attention this primary has received will likely boost turnout beyond the 2010 levels, though it's unclear by how much. It's probably only going to take between 10,000 and 15,000 votes to win on Tuesday. And given that Trump has an 82% favorable rating among Republicans in the district and by a 25 point margin voters think Grimm would work with Trump better, it's not hard to see how Grimm could get that number of votes.

4. A Grimm win is bad news for Republicans in the fall

Trump won the 11th district by 10 points in 2016, but Obama won it by 4 points in 2012. It's a district where Democrats can be competitive if a few things go their way.

A Grimm nomination would be something that would put Democrats in the ballgame. In talking with Grimm, he wanted to argue that he was the stronger general election candidate in the fall. The numbers don't agree.

In the Siena poll, only 55% of Donovan voters said they would support whoever won the Republican primary. Among Grimm voters, it was 81%. That is, Grimm voters were far more likely to back Donovan than the other way around. Even among Grimm's own voters, 22% agreed that Donovan was the stronger general election candidate.

That makes sense given that Grimm is a convicted felon. It also makes sense when looking at past election returns. Donovan won 62% of the vote in 2016, when House Republicans only won by 1 point nationally. Grimm took 55% of the vote in 2014, when House Republicans won by a significantly larger 6 points nationally.

Indeed, when you compare the presidential vote patterns to the results in 2014, Grimm's performance was among the weakest among Republican incumbents. His margin over his Democratic opponent was 7 points below what you expect given how all other Republican incumbents with Democratic opponents did. About 80% of Republican incumbents performed better given the lean of the district.

On the other hand, Donovan did about 6 points better than you'd expect given the lean of the district and how other Republican incumbents did in 2016. He outperformed about 85% of Republican incumbents given the presidential lean of the district.

Donovan winning the nomination would likely keep this seat in the Republican column. A Grimm victory on Tuesday would likely make this race a toss-up in the fall.