Federal air traffic controller union members protest the partial U.S. federal government shutdown in a rally at the U.S. Capitol in Washington, U.S. January 10, 2019.

The damage from the impasse over the president's demand for $5.7 billion to build his proposed border wall has only widened as it drags on. On Friday, about 800,000 federal workers will start to miss their second paychecks since the shutdown began last month. The GOP-held Senate will vote on dueling Republican and Democratic plans to fund the government Thursday , but both proposals are expected to fall short of the 60 votes needed to pass.

More of them believe President Donald Trump should compromise to end the partial closure than think congressional Democrats should give ground, according to new polls.

Americans want a way out of a record-breaking government shutdown that dragged into its 33rd day on Wednesday.

But asked about what action Trump should take, a larger proportion — 66 percent of Americans — say he should fund the government without wall money. Meanwhile, 31 percent believe he should reject a plan without spending for the barrier.

Asked what congressional Democrats should do next, 52 percent of Americans say they should agree to a bill with wall money to reopen the government, while 43 percent think they should refuse to approve the funds even if it means the shutdown will continue, according to a CBS News poll released Wednesday .

As the White House and Congress fail to find a solution, surveys suggest Americans want the stalemate to end — and they largely blame Trump for it. As Trump insists he will not give ground on the wall, the populace appears to favor a resolution that does not include money for the project, according to polls. The responses indicate that Trump has more to lose than Democratic leaders if the impasse continues to inflict harm on government workers and Americans who rely on services from housing and food assistance to airport security.

The poll also finds only 28 percent of Americans — and 56 percent of Republicans surveyed — believe the border wall is worth the shutdown. Seventy-one percent say it is not worth it. Thirty-seven percent of respondents think a wall is necessary to secure the U.S.-Mexico border, versus 61 percent who do not believe it is needed.

In a separate Morning Consult/Politico poll, 43 percent of registered voters said they support the construction of a border wall, while 49 percent responded that they oppose it. The survey shows backers of the president's barrier would be more willing to give ground than opponents.

Asked "if the only way to end the government shutdown" is to "dedicate funds for a border wall," only 7 percent of border wall opponents say they would support such a plan. Seventy-two percent responded that they would oppose it. Asked if they support putting money toward border security, but not a wall, to reopen the government, 34 percent of border barrier supporters say they would back such a proposal, while 51 percent say they would not support it.

Meanwhile, the surveys show Americans are concerned about the damage caused by the shutdown. Sixty percent of respondents to the CBS poll responded that the shutdown is "causing serious problems." Another 34 percent say the funding lapse is "causing some problems, but they are not serious," while 5 percent think it is "not causing problems."

Nearly half of registered voters — or 46 percent — responding to the Morning Consult/Politico survey called the closure a "crisis" and 35 percent considered it a "problem." Only 9 percent said it is "not a crisis or a problem."

The same pool of voters largely blame Trump for the closure of about a quarter of the government. Forty-nine percent of respondents say the burden falls on the president, while 35 percent point the finger at Democrats in Congress. Only 4 percent blame Republicans in Congress.

In a series of tweets Wednesday, Trump insisted on funding for his proposed barrier. The president said he sees "great unity in the Republican Party" on support for the wall. Still, several GOP senators have pushed for a bill to temporarily fund the government while Republicans and Democrats hash out a border security deal.

As Trump appears to be losing the messaging battle on the barrier, he tried out a new argument on Wednesday. He tweeted: "BUILD A WALL & CRIME WILL FALL!" The president called it the "new theme" of the Republican Party.

On Thursday, the Senate will hold its first procedural votes on ending the government shutdown since funding for nine departments lapsed on Dec. 22. The first plan it will take up reflects Trump's offer to put $5.7 billion toward the wall in exchange for three-year extensions of legal protections for more than 700,000 immigrants brought to the U.S. illegally as children and migrants fleeing humanitarian crises.

Democrats have slammed that plan, which likely will not get through the Senate. On Tuesday, Trump also lost leverage in trying to use the Obama-era Deferred Action for Childhood Arrivals policy to force Democrats' hand. The Supreme Court is unlikely to take up a case about the legality of the Trump administration's decision to end DACA during its current term, likely leaving it in place into 2020.

If the GOP plan fails Thursday, the Senate will take up a Democratic-backed proposal to reopen the government through Feb. 8 while lawmakers negotiate a broader deal. It is similar to bills already passed by the Democratic-controlled House. The measure will likely fail, as well.

It is unclear how Trump and Congress would proceed if those proposals cannot get through the Senate.

The CBS News telephone poll surveyed 1,102 adults nationwide. It is unclear what exactly its margin of error is.

The Morning Consult/Politico poll surveyed 1,996 registered voters online and has a margin of error of plus or minus 2 percentage points.

Correction: This story has been updated to reflect the correct sample of voters in two of the Morning Consult/Politico poll questions.

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