Senate Majority Leader Mitch McConnell said Tuesday that Republicans are prepared to go it alone on tax reform, saying the GOP and Democrats are too far apart on basic principles to even try for consensus.

He was responding hours after Democrats laid out their red lines, saying they want to cooperate but will work only on plans that don’t benefit the wealthy or increase the deficit.

Those are nonstarters for Republicans, who say that tax rates must be cut across the board to get the economy roaring and that trumps even the growing deficit.

“I don’t think this is going to be 1986, when you had a bipartisan effort to scrub the code,” said Mr. McConnell, Kentucky Republican.

The White House has set an aggressive timetable for getting a deal done this year, and Senate Republicans said that means turning to the same fast-track budget procedure that they tried to use for their failed Obamacare repeal and replace effort.

The reconciliation process allows bills to pass without facing a Democratic filibuster, but it would constrain the GOP’s ability to write a lasting overhaul that doesn’t deepen the deficit.

Mr. McConnell said there might be a few Democrats willing to reach across the aisle, but he explicitly rejected Senate Democrats’ other demand that Republicans forgo reconciliation.

Senate Minority Leader Charles E. Schumer kicked off the day with a letter, signed by most of the Democratic Caucus, laying out his party’s principles for getting involved.

They said they will not support any plan that cuts taxes for the top 1 percent or an effort to pass “deficit-financed tax cuts,” and said reconciliation would be a recipe for Republicans to jam through “partisan short-term tax cuts.”

Mr. Schumer said the GOP should have learned its lesson after going it alone on health care, only to see their bill collapse when they couldn’t even muster support within their own conference.

“There’s a real potential for bipartisan support on tax reform, but I think our Republican colleagues — dictated by the Koch brothers, hard-right wing of their party — is running away from it,” said Mr. Schumer, New York Democrat.

Three Democrats did not sign onto Mr. Schumer’s new letter. Each of the three — Sens. Joe Donnelly of Indiana, Heidi Heitkamp of North Dakota and Joe Manchin of West Virginia — face tough re-election fights next year in states President Trump won easily.

The offices of Mr. Donnelly and Ms. Heitkamp did indicate Tuesday that the senators stand ready to work on the issue on a bipartisan basis.

Mr. Manchin said he is likewise holding out hope for a bipartisan deal, saying it would be “kind of hard” for Republicans to pass a package without reaching out to Democrats.

“It works better if we work together. It always has,” he said.

“The most important thing is … no more debt. My God, we got enough debt. Can’t we do something that doesn’t increase the debt?” Mr. Manchin said.

Senate Finance Committee Chairman Orrin Hatch, a key tax-writer, did say he would prefer not to use the reconciliation process, if possible, and that he thinks tax reform can get done this year.

“But it’s going to take a bipartisan effort,” the Utah Republican said.

Republicans say a major sticking point is the size of the tax cuts, and therefore the amount of additional deficits that would pile up.

“If you have no ability to use the short-term deficits to grow your economy, then you’re basically starting the conversation off at a hard no,” said Sen. Tim Scott, South Carolina Republican.

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