(CNN) President Donald Trump was bragging this week about a surprising bump in one poll, but his optimism missed the fact that recent polling is in agreement that his approval ratings have taken a hit during the month-plus partial government shutdown and the public largely blames him for the country's predicament.

On average, Trump's approval rating in the month of January -- during the longest shutdown in US history -- stands at 37% approve and 57% disapprove, down from his average of 41% approve and 51% disapprove in late November to early December (pre-shutdown), according to a new CNN Poll of Polls released Wednesday.

CNN's Poll of Polls is an average of surveys among adult Americans aggregated to give a more well-rounded view of public opinion.

But there are are noteworthy findings in the individual polls as well. CBS News released a poll Wednesday showing Trump with 36% approval, his lowest of all polls this month. Additionally, 71% of Americans said that building a wall along the border with Mexico isn't worth shutting down the government, and most (61%) said the border can be secured without building a wall. Even the GOP isn't totally behind the President on the issue; a majority of 56% of Republicans said the wall is worth shutting the government down and 43% said it isn't. Seven-in-ten independents and 92% of Democrats agreed that it isn't worth the shutdown.

With Trump's approval on the downswing, the polls are also showing people blame him for the shutdown ; in each of the four polls that asked respondents to place blame, majorities said blame lies with the President, while about a third in each poll cited Democrats in Congress as primarily responsible. As of Wednesday, the government shutdown has been going for 33 days and sets a new record each day. The Senate is set to convene Thursday to vote on two bills -- one backed by Republicans and the other by Democrats. Both are expected to fail.