A majority of voters believe 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's proposal to link funding for the border wall with temporary protections for some undocumented immigrants should be the starting point for negotiations over the government shutdown, a new poll released Tuesday showed.

The Hill-HarrisX poll found that 56 percent of voters aware of Trump's proposal believed that the president's offer should be taken as a "good faith" offer to start negotiations over a partial government shutdown that is now in its fifth week.

Forty-four percent of respondents said it was not serious offer and that congressional Democrats should reject it.

By a margin of 55-45 percent, a majority of independent voters said they believed Trump's proposal was something Democrats should consider to be a starting point.

Trump on Saturday floated extending protections for Deferred Action for Childhood Arrivals (DACA) program recipients for three years and a three-year extension of protections for Temporary Protected Status (TPS) holders in exchange for more than $5 billion for a border wall.

Previous polls have shown more voters blame Trump for the shutdown than Democrats.

Democratic leaders signaled both before and after Trump's Saturday speech that they would not enter into any sort of border negotiations with the president unless he agreed to fully fund the government beforehand.

Trump and other Republicans have rejected this Democratic demand, saying reopening the government would remove leverage from the president's positioning.

"Where's the leverage for the president in terms of getting them to move on the issue of the day?" Sen. David Perdue (R-Ga.) told CNBC on Wednesday when asked about the idea of ending the shutdown before starting immigration negotiations.

Trump's offer to negotiate with Democrats is also opposed by some conservatives, including far-right pundit Ann Coulter and Rep. Steve King Steven (Steve) Arnold KingGOP leader: 'There is no place for QAnon in the Republican Party' Loomer win creates bigger problem for House GOP Win by QAnon believer creates new headaches for House GOP MORE (R-Iowa), who have accused the president of bending to Democratic pressure.

In a Tuesday tweet, Trump wrote that he had made "no Cave" on the issue but rather that congressional Democrats "want to play political games."

On Tuesday, Sen. 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.) announced that he would hold a formal Senate vote on Trump's latest proposal. The GOP Senate Majority Leader has indicated throughout the immigration stand-off that he would not allow legislation to come to a vote that the president did not support.

"The opportunity to end all this is staring us right in the face. That's why we'll vote on this legislation on the Senate floor this week. All that needs to happen is for our Democratic colleagues to agree that it's time to put the country ahead of politics, take yes for an answer and vote to put this standoff behind us," McConnell said.

The Hill-HarrisX survey was conducted Jan. 21-22 among 999 registered voters by HarrisX. The sampling margin of error of the poll is 3.1 percentage points.

—Matthew Sheffield