“We have discovered a sensitivity and a vulnerability by using this method, and we’re going to do it a whole lot more,” said Sen. Tim Kaine (D-VA), an author of the Venezuela resolution.

The plans come after Trump was forced to offer assurances this week to flip two Republicans crucial to avoiding another embarrassing setback by squashing a bipartisan resolution that would have curbed further military actions in Venezuela without Congress. Such measures require floor votes, against the wishes of Republican leaders, and only need a simple majority.

“They do put some pressure on Republicans,” Kaine went on to say to the Washington Examiner. “But we also feel like the prospect of these votes causes the administration to take some important steps that he otherwise wouldn’t take.”

The White House made personal commitments to sway the minds of Sens. Josh Hawley (R-MO) and Todd Young (R-IN), who days earlier voted with all Democrats and three other Republicans to advance the resolution that would have limited Trump’s unilateral military capabilities following the U.S. capture of former Venezuelan dictator Nicolas Maduro.

Those promises included letters from Secretary of State Marco Rubio to Young and Foreign Relations Committee Chairman James Risch (R-ID) confirming there were no U.S. armed forces currently in the South American country and that Trump would seek congressional authority or give written notification should the situation change. Hawley cited Rubio’s assurances as satisfactory, and Young said he also secured public congressional testimony from Rubio that will occur after next week’s Senate recess.

“This is not a mandate on the president. It’s merely an effort to kind of reset our work on war powers,” Young told the Washington Examiner. “I feel like the message was received, which is what I wanted to happen. I felt like I got some concrete and important deliverables out of it.”

But aside from Greenland, there is likely to be even less GOP appetite to buck Trump on other countries, yielding less leverage for Democrats to score measured wins through their Republican colleagues. The Venezuela vote required Vice President JD Vance to cast his eighth tiebreaker. Unlike Venezuela, Trump has only expressed threats regarding Iran, Cuba, Colombia, Mexico, and Greenland. Last month, Trump struck Islamic State group targets in Nigeria.

Hawley and Young were noncommittal on forthcoming war powers measures and said they would evaluate each country on a case-by-case basis.

“I’m not interested in helping [Democrats] with their politics,” Hawley told the Washington Examiner. “I’m interested in making sure that No. 1: we protect the country. No. 2: the Constitution’s followed. And listen, I support the president, and he and his team were great to work with on this.”

Democrats are bullish that a vote on Greenland could prove even more difficult for Republicans than Venezuela, given Trump’s escalating rhetoric in seizing the NATO ally by military force. Officials from Greenland and Denmark met with high-level administration officials and lawmakers in Washington in recent days, including Vance and Rubio.

Sen. Lisa Murkowski (R-AK), who voted with Sens. Susan Collins (R-ME), Rand Paul (R-KY), and Democrats to limit Trump’s authorities in Venezuela, was noncommittal on her position with a Greenland resolution but noted she’s been “consistent” in recent months in her support for previous war powers resolutions on Venezuela.

“I don’t even like to think about a war powers resolution with Greenland in it,” Murkowski told the Washington Examiner.

VANCE HELPS SQUASH VENEZUELA WAR POWERS PUSH IN SENATE, STAVING OFF SECOND TRUMP REBUKE

But others, such as Sen. Thom Tillis (R-NC), despite echoing the concerns of Collins and Murkowski about Trump’s Greenland rhetoric, have downplayed the need to address it with what they characterize as unnecessary preemptive action by Congress. And another possible handicap to Democrats’ success is their healthy dose of skepticism that the administration will keep the promises it has made to members of its own party.

“We are wise to be wary about commitments by these guys,” Kaine said. “But when they’ve made them — and they’ve made them publicly — all senators can monitor to see whether they actually live up to them.”