President Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE and congressional Republicans are trying to change the narrative on Democrats as the partial shutdown drags into its fifth week.

Republicans, who have seen poll after poll showing that a majority of respondents blame Trump for the shutdown, are eager to corner Democrats by forcing a vote on the White House proposal to reopen the government and provide Trump with $5.7 billion in wall funding.

Whether the gambit works is anyone’s guess.

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Senate Democrats are showing no signs of division so far, and the Senate is also poised to vote Thursday on another measure that would temporarily reopen the government but not provide funding for the wall.

Still, the votes on Thursday could allow Republicans to argue that they are putting up proposals to end the shutdown after weeks in which the only actions to do so have been taken by Democrats in the House.

After watching House Democrats pass those bills for more than four weeks, Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE (R-Ky.) is eager to flip the script and have Democrats vote “no” on a bill to reopen the government — a day before federal workers impacted by the funding lapse will miss their second paycheck.

The White House and McConnell have also sought to sweeten the pot: Their plan includes priorities backed by Democrats including extension of the Violence Against Women Act and more than $12 billion in disaster relief funding.

Neither proposal is expected to get 60 votes without a dramatic U-turn by either Trump or Democrats. But holding the two votes will allow Republicans to try to change the media narrative and counter the Democratic strategy of forcing McConnell to repeatedly block the House bills.

It could also be a win-win situation for Republican senators, since it allows those representing red states to vote for Trump’s proposal, while purple-state senators such as Sens. Susan Collins Susan Margaret CollinsSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (R-Maine) and Cory Gardner Cory Scott GardnerSenate Republicans face tough decision on replacing Ginsburg What Senate Republicans have said about election-year Supreme Court vacancies Chamber of Commerce endorses McSally for reelection MORE (R-Colo.) could vote for the clean three-week stopgap measure.

Multiple polls have shown that a majority of respondents are blaming Trump and congressional Republicans for the partial shutdown, which is the longest funding lapse in modern history.

In the latest The Hill-HarrisX survey, 46 percent of registered voters who responded and identify themselves as political independents said that Trump and the congressional GOP are primarily responsible for the government closure, a 7-point jump from a Dec. 30-31 survey.

But Trump is showing no signs of shifting his strategy in response to polling or grumbling by moderate lawmakers.

The president views the battle with Democrats over the wall as too important to lose and is convinced the 33-day shutdown has helped make his case to the public why a wall is needed to end what he sees as a crisis of illegal immigration and drug smuggling at the U.S.-Mexico border, according to a source who requested anonymity to discuss the White House’s internal thinking.

Trump is expected to meet this week with a group of conservative leaders to get input on immigration proposals and possibly push toward a broader immigration agreement if the shutdown ends.

The source added that Trump does not care about the polls and is feeling no pressure to cave on his demands.

The president is not closing off the possibility of supporting permanent extensions for the Deferred Action for Childhood Arrivals (DACA) program and Temporary Protected Status (TPS) as part of an immigration deal with Democrats.

Trump attempted to end the Obama-era DACA program for young immigrants but was blocked by federal judges from doing so. The Senate immigration deal contains a temporary extension of the program for existing beneficiaries. TPS benefits migrants from disaster-stricken or conflict-ridden countries but Trump has sought to wind down the program for several nations.

The source said that such a concession would have to be in exchange for the right package of border security measures and changes to immigration law and cautioned Trump is unlikely to back anything that does not have a chance to win 60 votes in the Senate, which is controlled by Republicans.

Trump praised McConnell on Tuesday and pledged that he will not “cave” to the demand from Democrats to reopen the government and then negotiate.

“Never seen [McConnell] and Republicans so united on an issue as they are on the Humanitarian Crisis & Security on our Southern Border!” Trump said in a tweet.

Some GOP senators over the weekend suggested that Trump’s offer should be viewed as an opening salvo to jumpstart negotiations that have otherwise been stalemated after a White House meeting earlier this month.

But the White House is not planning to make a second offer to Democrats if the president’s proposal fails to pass the Senate this week, according to the source, indicating they believe it is incumbent upon Democrats to make the next move.

Democratic leaders show no signs of backing down. Senate Minority Leader Charles Schumer Chuck SchumerPelosi orders Capitol flags at half-staff to honor Ginsburg Ginsburg in statement before her death said she wished not to be replaced until next president is sworn in Democrats call for NRA Foundation to be prohibited from receiving donations from federal employees MORE (N.Y.) on Tuesday said the White House’s proposal is “going nowhere fast.”

“Everyone knows the president said he would be proud to shut down the government. Everyone knows that he and Leader McConnell are the only obstacles to opening it back up. Across the board, the polling shows it,” Schumer said from the Senate floor.

The White House plan would need at least seven Democratic votes to overcome the 60-vote filibuster.

Sen. Joe Manchin Joseph (Joe) ManchinBiden promises Democratic senators help in battleground states Senate leaders quash talk of rank-and-file COVID-19 deal OVERNIGHT ENERGY: House Democrats tee up vote on climate-focused energy bill next week | EPA reappoints controversial leader to air quality advisory committee | Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' MORE (D-W.Va.) said over the weekend that he was “hopeful” Trump’s plan would “allow us to immediately reopen” the government. A spokesman for the centrist Democrat said Tuesday that he is undecided about how he will vote on the president’s plan.

Sen. Doug Jones (D-Ala.) will also face intense pressure to back the president as he runs for reelection in a state Trump won by nearly 30 points. Jones said at a town hall in Alabama over the weekend that Trump’s plan was a “hopeful sign” and that he thought he saw “movement” in the funding fight.

A spokeswoman for Jones didn’t respond to a question Tuesday about how he will vote.

Meanwhile, tensions between Speaker Nancy Pelosi Nancy PelosiPelosi: Ginsburg successor must uphold commitment to 'equality, opportunity and justice for all' Bipartisan praise pours in after Ginsburg's death Pelosi orders Capitol flags at half-staff to honor Ginsburg MORE (D-Calif.) and Trump escalated further Tuesday when the White House signaled it wants to move forward with a Jan. 29 State of the Union speech even though he doesn’t have approval from Congress.

House Democrats are expected to pass a package of six additional spending bills already backed by Senate Republicans. While they’ve largely been unified during the partial shutdown, some cracks have begun to form in the Democrats’ armor.

Some Democratic freshmen in a letter to Pelosi and party leaders pressed them to promise a vote on border security measures — including Trump’s wall — as a condition of reopening the government. The letter, spearheaded by Rep. Elaine Luria Elaine Goodman LuriaVirginians wait up to four hours to cast early voting ballots US Chamber of Commerce set to endorse 23 House freshman Democrats House panel votes against curtailing Insurrection Act powers after heated debate MORE (D-Va.), was first reported by Politico.

And on Tuesday, Rep. Collin Peterson Collin Clark PetersonThe Hill's Campaign Report: 19 years since 9/11 | Dem rival to Marjorie Taylor Greene drops out | Collin Peterson faces fight of his career | Court delivers blow to ex-felon voting rights in Florida Peterson faces fight of his career in deep-red Minnesota district Democrats for Life urge DNC to change party platform on abortion MORE (D), a Minnesota Blue Dog, told a local radio station that Democrats should “give Trump the money” he wants for the border, saying the project is ultimately inevitable.

“Why are we fighting over this?” he told KFGO. “We’re going to build that wall anyway, at some time.”

Mike Lillis and Jordan Fabian contributed to this story.