Finally, they want a rewrite of the tax code that does not add to the deficit and is not paid for with cuts to programs such as Medicare, Medicaid and Social Security.

For much of this year, Democrats have criticized the proposed tax policies of Republicans as giveaways to the rich. It was clear on Tuesday that Republicans are not eager to let Democrats meddle with their plans for a tax overhaul, even if they would welcome a few of their votes.

“We will need to use reconciliation because we have been informed by the majority of the Democrats in a letter I just received today that most of the principles that would get the country growing again, they’re not interested in addressing,” Mr. McConnell said, leaving the option for Democrats to support a Republican-led tax plan. “So I don’t think this is going to be 1986 when you had a bipartisan effort to scrub the code.”

For its part, the Trump administration has been more vocal this week about the importance of attracting some Democrats to its tax plan. At a gathering on Monday of conservative activists sponsored by Americans for Prosperity, the political network of the Koch brothers, Marc Short, the White House legislative affairs director, made the case that Democrats need to be brought into the fold. The Republican majority in the Senate, he said, was too slim for party members to count only on one another.

“We ask your help, actually, reaching out to Democrats as well,” Mr. Short said, noting the ones who are coming up for re-election. “If they hear from their constituents that they need tax reform, that’s going to be a very strong selling point.”

It remains unclear how enthusiastic Democrats really would be to make compromises with Republicans that would allow Mr. Trump to score a major legislative victory. In the battle over the Affordable Care Act, even potentially vulnerable Democratic senators from states that the president won last year held firm in their opposition to the repeal of the health care law.

Relegated to the minority, however, Democrats are trying to stake out the moral high ground. Mr. Schumer warned on Tuesday that Republicans could suffer the same fate on taxes that they did on health care if they continue to operate alone.