That's a tough situation to be in, and unfortunately, it's not all that uncommon these days.  People are so overcommitted (especially if they have school aged children) and stressed out over other things (COVID, fuel prices, etc.) that it's hard to get them to take on yet another responsibility.  Still, it's encouraging that your members do want the association to continue.

Our daughter's road association went through a similar crisis years ago.  They had about 35 members in a non-profit road association.  Then the Secretary burned out and handed the job to our daughter, who had only recently moved in.  Shortly after that, the President showed up on our daughter's porch and handed her a box of files and said, "You'll make a great president.  I'm headed for California."  It got to where they couldn't do anything at annual meeting because their bylaws required a quorum, and not enough people showed up.  Without a functioning association, the road started to deteriorate, and no one wanted to pay dues that produced no visible improvement in the road.  It got to where only nine people out of the 35 paid their dues, and it wasn't enough to even cover the plow bill.  They ended up scrapping the non-profit and starting over as a statutory association, with new bylaws that do not require a quorum at annual meeting.  That allowed those who did show up to hire contractors to plow and maintain the road, and as things started improving, people began to participate again.  They now have nearly everyone paid in full, but getting people to serve on the Board is still a challenge.

Looking at the statutes, I see that it says a road association "may choose a commissioner or board."  I see nothing in the statute that says you have to have a board, or that specifies how many members the board must consist of, or what offices they must hold.  Where you have such a small association, and where members want the association to continue but are unwilling to serve, you might consider changing your bylaws so you have a smaller board, or even just a commissioner.  Or you could change the bylaws to quote the statute, allowing you to have a commissioner OR board, which would allow you flexibility in case the situation changes from year to year.

You might also want to look at MARA's Resources page, paragraph 7c, for notes on Encouraging Member Participation.  Maybe it will give you some ideas.  And if you find something that works, let us know!  Other people may look at this thread when they have a similar problem.

Your board may or may not be correct about the enforceability of its road improvement cost assessments, but let’s take that at face value for now.

To address your questions:

Assessment without a signed construction contract?

To sign a contract without the funding in hand could expose the association to the obligation to perform under the contract or suffer financial consequences.  Also, major road improvement costs exceed normal maintenance costs and should be treated separately from operational costs even when included in an annual budget.  So, I do not find it unusual that your board has made an assessment for a major improvement without a signed contract or that they did so as a separate topic and not part of an annual budget. But that is just my opinion based upon my leadership experience.

Are owners required to pay?

Public Law 2021 Chapter 13 (LD192) “An act to Define the Responsibilities of Residential Property Owners For the Maintenance and Repair of Private Roads” (Effective June 29, 2021) changes the landscape a bit.

That law was added to Title 23 as §3121 - read it on the Resources page (Item 2C) and notice that it includes “…reasonable and necessary repairs…determined pursuant to the terms of any agreement entered into to determine the share of the cost of reasonable and necessary repairs…” and that costs must be paid “…after reasonable due process and notice…” and it applies to “….any road association created pursuant to this chapter or otherwise….” (emphasis added)

Your association’s proposed improvements are necessary and benefit all owners. The membership approved the assessment at so there was at least some “due process” and while some members of your association may consider the process flawed, challenging the assessment based upon a flawed process might not result in a positive outcome.

The law is new, and I believe still untested. The first paragraph clearly states that whenever an agreement does exist and in whatever form, it is enforceable and there are no caveats in that paragraph.  Perhaps your board should consult with an attorney experienced in road association matters to see if §3121 affords them the enforcement authority they thought they do not have.