The White House said Wednesday that a number of Democratic senators have called for President Trump’s Supreme Court nominee Judge Neil Gorsuch to be treated fairly by receiving a hearing and an up-or-down vote.

The lawmakers themselves, however, say that doesn’t necessarily mean they won’t join a filibuster to block Judge Gorsuch.

Whether Democrats will mount a filibuster, and how many of them would join in, is the consuming question on Capitol Hill.

Liberal groups are cheering on the prospects of a filibuster, while conservative groups, eager to drive a wedge between Democratic lawmakers and their base, are trying to force vulnerable Democrats to take a stance.

So when Sen. Jeanne Shaheen went to the chamber floor Tuesday night to speak, saying “everybody I’ve talked to agrees he should [receive] a hearing and an up-or-down vote,” conservatives counted her as another Democrat unwilling to filibuster.

“We hope more Democrats will continue to join their colleagues in fulfilling their constitutional duty to offer advice and consent on the president’s nominee,” White House press secretary Sean Spicer said Wednesday.

Brian Rogers, executive director at America Rising Squared, a conservative pressure group, said Ms. Shaheen was “breaking” with Democratic leaders’ plans for a filibuster.

Ms. Shaheen’s office, though, said she hasn’t ruled that out and Republicans are misconstruing her words.

The senator herself took to Twitter to correct the record.

“To be clear @PressSec, I meant a cloture vote,” Ms. Shaheen tweeted.

The same was true for Sens. Richard J. Durbin, Richard Blumenthal and Joe Manchin III — all Democrats who had also called for a vote on Judge Gorsuch.

A decade ago, the term “up-or-down vote” was used to mean a majority vote, as opposed to a filibuster vote, which required 60 senators to overcome the blockade.

But after Republicans’ refusal to even allow a vote on Judge Merrick Garland, President Obama’s Supreme Court pick, Democrats are using “up-or-down vote” to mean a vote at all — in contrast to Judge Garland.

Mr. Rogers said that was “disingenuous.” He counts nine Democrats he said have called for “a vote” on Judge Gorsuch, and said if they end up supporting a filibuster, they will be going back on their word.

Carrie Severino, chief policy director at the conservative Judicial Crisis Network, said the Democrats are trying to please both the “radical left fringe” of their base who wants obstruction during Mr. Trump’s presidency, and the majority who would like to see the nominee get an up-or-down vote.

“They’re trying to sound moderate, while trying to sound tough and partisan at the same time It’s not very effective,” Ms. Severino said. “This is not confusion of, ‘Oh, we just don’t understand how the system works.’ This is intentionally misleading.”

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