Is it wise for the Republican party to stand with Trump?

The Trump administration is not likely to make any compromise in any near future while the Democratic party does not want to make any compromise by giving any fund for the president's wall. Under such circumstance, the US government shutdown will continue for more days or even weeks. When we see the voting in the US Congress, it is clear that the Democratic party is uniting to fight against Trump's idea of a border wall and the Republican party is fighting against the Democratic party. According the polls, shutting down the government for building a border wall is not a popular move and most people blame the Trump administration for the government shutdown, though the polls do not always accurately show the population opinion. Let's assume the polls correctly show the public opinion this time, why is the Republican party supporting President Trump in the Congress?

The politicians elected by the people should serve the interests of their constituencies; however, some constituencies which have Republican politicians elected also suffer the US government shutdown, and their representing politicians  in the Congress do not seem to protect their interests. There are various reasons to explain this. On one hand, it could be just a play of pure bipartisan politics that one party agrees and the other party disagrees. On the other hand, it could serve the best interest of the Republican party. First, if the bill cannot be passed by the Congress, then the president does not need to reject the bill, this will reduce the criticism about their Republican president, Trump. Secondly, when the two parties are fighting in the Congress, people may not take a side and blame the other side, since the chaotic situation makes everyone responsible for the government shutdown. Thirdly, though we see some people suffer the government shutdown, there could be a lot more people supporting Trump's wall plan or simply supporting Trump, this person, then it makes a lot of sense for the Republican party to support the president and back the wall plan. Fourthly, though the wall plan may not be popular, it does not mean standing with the Democratic party in these Republican controlled constituencies is popular.

Overall, the tension between the Republican party and the Democratic party is mostly about the bipartisan politics, and could serve the interests of the Republican party, though it seems unpopular.