It's not clear to me that Democrats are opposed to border-wall construction (your one source suggests they are fine with border walls/fences where necessary), so much as they opposed to some of the plans for full-border walls that have been put forth so far.
Recently, in response to reports that the spending bill would include funding for a border wall, 5 Democratic senators released a letter voicing concerns over the cost, the effectiveness, and the legal issues of constructing it.
We are also concerned with reports that there may be an effort to include funding for a very expensive new wall along the southern border with Mexico and a “deportation force.” According to non-partisan experts, the proposed new border wall could cost as much as $25 million per mile and raises considerable issues that have not been resolved by the Congress or the Department of Homeland Security. First, many experts believe that such a border wall will not work. Second, there is real concern that the Administration, put simply, has no plan to build the border wall. For example, the Administration has not detailed how to 1) use eminent domain and other procedures to acquire land from private landowners and Native American tribes, 2) design the wall, 3) locate the wall, 4) construct the wall, and 5) require Mexico to pay for the wall given the President’s clear and repeated promises that he would force Mexico to do so. Finally, there are objections to the construction of a wall from Democratic and Republican members of Congress that represent border states. Given these and other concerns, we believe it would be inappropriate to insist on the inclusion of such funding in a must-pass appropriations bill that is needed for the Republican majority in control of the Congress to avert a government shutdown so early in President Trump’s Administration.
Senator Charles Schumer
Senator Richard Durbin
Senator Patty Murray
Senator Debbie Stabenow
Senator Patrick Leahy
Based on this letter, it appears their main objections to a full border wall are currently the cost-benefit ratio and the legal issues of taking land from Americans to build it on; objections that may not be unique to Democrats.