Republicans have been talking all year about tax reform, but primarily amongst themselves.

Party leaders are now aiming to privately craft a detailed tax plan, which they then want congressional tax-writing committees to start working on after Labor Day.

But so far Democrats have largely been excluded from the process.

On Tuesday, 45 Senate Democrats issued a letter to Senate Republicans, outlining the three basic priorities a tax reform package must meet to garner their support.

Such a package, they say, should:

Not increase the tax burden on the middle class, nor should it benefit the wealthiest individuals.

Go through "regular order," meaning it will be subject to plenty of hearings, have input from both parties and be subject to a 60-vote threshold in the Senate. In other words, not the "fast track" process known as reconciliation Republicans used to try to repeal Obamacare, which only required 51 votes to pass, but failed anyway.

Be fiscally responsible and not add to deficits.

To stress their point, Senate Minority Leader Charles Schumer on the floor Tuesday morning, said, "we will not support any effort to rewrite the tax code to give another tax break to the top 1% or add even more to the deficit and debt."

The letter garnered a sharp rebuke from Senate Majority Leader Mitch McConnell, who told reporters that Republicans would have to use the fast-track process "because we have been informed by a majority of the Democrats ... that most of principles that would get the country growing again, they're not interested in addressing."

Related: Most conservative House members list tax reform demands

Tax experts have stressed to lawmakers that tax reform tends to work best and last longer when negotiated in a bipartisan way.

But finding agreement on tax reform is notoriously difficult.

Even Republicans themselves are divided over whether and how tax reform should be "paid for." And to the extent they choose to pay for it, it's not clear if they'll simply lean on optimistic growth assumptions to offset the cost of tax cuts.

As for the middle class, Republicans say they want to simplify the code for the average tax filer and offer middle-class tax relief of some kind. So there may be room for some agreement with Democrats on that front.

But how the rich are taxed could be the biggest source of contention.

Treasury Secretary Steven Mnuchin has said that while high-income households may see a cut in their top income tax rate, many won't actually pay less because a lot of their deductions would go away.

Without an actual bill on the table, however, it's impossible to say if he's right.

And the wealthy could potentially benefit a great deal if lawmakers lower business tax rates for corporations and smaller businesses and partnerships. Republicans argue business tax cuts create more jobs and raise wages, and will be a win for the average American.

Related: Will a corporate tax cut benefit the middle class?

So can they find common ground? At least one leading Republican thinks it may be possible. Maybe.

Before McConnell's statement, Senator Orrin Hatch, who runs the Senate Finance Committee, told reporters "I don't want to do tax reform [with] reconciliation if we can avoid it. I'd like to do it just straight up without it. I think we can."

Given how hard it is to garner agreement on the actual details of tax reform -- none of which have been decided yet -- and given how hard it's been for Republicans to unify their caucus, even if Republicans use reconciliation rules, some Democrats' votes just might be needed to push tax reform over the finish line. That is, if Democrats are willing to support it.

-- CNN's Ashley Killough and Ted Barrett contributed to this story

Correction: An earlier version of this story incorrectly attributed a quote from Orrin Hatch to Mitch McConnell.