Senate inoriajority Leader Mitch McConnell (R-Ky.) is threatening more Iran votes this week. (Photo by Chip Somodevilla/Getty Images)

Senate Democrats on Tuesday blocked a second Republican attempt to pass a resolution disapproving of the Iran nuclear deal.

But Senate Majority Leader Mitch McConnell (R-Ky.) is hardly giving up the fight, moving to schedule a Thursday vote on rolling back sanctions on Iran until the Islamic Republic recognizes Israel’s right to exist and releases American prisoners being held in the country. That set includes The Washington Post’s Iran correspondent, Jason Rezaian.

It’s a tactic aimed at forcing an up-or-down vote on the nuclear pact and getting Democrats directly on the record supporting what Republicans hope will be politically unpopular. The deadline for congressional action on the deal is Thursday — Sept. 17.

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Negotiators kept questions of Iran’s nuclear ambitions separate from the myriad other complaints that Washington has with the regime when striking the multilateral nuclear pact. But McConnell defended his strategy, saying: “Linkage is appropriate, and in this negotiation, it would have been wise to have linkage.”

“The American people deserve to know where their senators stand on the prospective deal,” McConnell said.

The majority leader switched gears on Tuesday after bringing up an exact repeat of the measure Senate Democrats struck down last week. It failed, 56 to 42, with 60 votes needed to get around the Democratic filibuster.

Senate Republicans aren’t pretending they can defeat the Iran deal. It has been clear for weeks now that Democrats had at least enough votes to sustain the president’s veto.

But Senate Republicans are trying to make the votes as politically painful as possible.

To that end, McConnell on Tuesday threatened to change the terms of the disapproval resolution if Democrats do not allow an up or down vote on the deal.

Democrats heading out of the vote Tuesday didn’t think McConnell’s new strategy would affect pro-deal Democrats’ willingness to stick together and oppose future procedural motions on the resolution of disapproval.

“Oh no no no,” said Sen. Tom Carper (D-Del.), when asked if the new language would affect his vote.

“No,” Sen. Claire McCaskill (D-Mo.) said flatly. McConnell “just needs to do something to get you guys to cover Groundhog Day.”

Democratic leaders have decried the lineup of repeat Iran votes as pointless.

“With a looming government shutdown, the Republican Leader has already wasted far too much time,” Senate Minority Leader Harry Reid (D-Nev.) said. “But by the look of this week’s schedule, the Republican leader doesn’t seem to be in any hurry to avoid a shutdown…the Senate will waste precious time on another failed vote. And then what comes next?”

But Republicans defended their plan and are showing few signs of giving up the fight.

“There’s just a significant amount of frustration that we’re not able to get an up-or-down vote,” said Senate Foreign Relations Chairman Bob Corker (R-Tenn.).

Mike DeBonis contributed to this story.

Correction: A reference to Senate Majority Leader Mitch McConnell (R-Ky.) mistakenly identified him as the “minority” leader in a previous version of this article, which has been corrected.