What does “get rolled” in “Eight ways Trump got rolled in his first budget negotiation” mean?

Solution 1:

Especially because this is a headline, it could be a compressed use of the figurative term "steamrolled."

On April 25, Politico ran a similar headline: Ryan likely to get rolled on tax reform.

The content of the article begins:

Donald Trump is set to steamroll Paul Ryan on tax reform, the issue the speaker has devoted his political career to achieving. But don’t expect Ryan to relinquish his pet cause easily.

Unlike the Politico piece, the Washington Post uses the word "rolled" only in the headline, not in the content, so we can only speculate, but evidently using "rolled" as a condensed form of "steamrolled" has recent precedent.

In this sense, either to "roll" or to "steamroll" means to best an opponent or force them in a particular direction against their will. See definitions below.

The terms are sometimes used interchangeably in sports reporting as well. In this recent example, there is no mention of who is getting rolled, but the use of "roll" in the headline appears to be shorthand for "steamroll" based on the subheading:

Headline: "Bulldogs roll their way to Sulphur"

Subheading: "Behind their two LSU-Eunice signees, Ascension Catholic was able to dominate Catholic of Pointe Coupee from start to finish and steamroll to a 10-1 victory that pushed them through to the semifinals after falling in the quarterfinals for three straight seasons.

• Donaldsonville Chief, May 3, 2017

MacMillan offers this definition of steamroll:

To defeat or destroy an opponent completely.

OED also offers a figurative definition and example of "steamroll" in this context:

(b) fig.; (also) to force or drive in a given direction (cf. steam-roller v. 2).

1975 Times 21 July 1/8 The ruling party..will steamroll the endorsement through.

It is not uncommon in headline writing to colloquialize or abbreviate expressions to make a concise point, especially in a piece as informal as the Post article in question. My interpretation of the headline is that Trump got steamrolled by the Democrats.

Solution 2:

Roll is one of those words with dozens of different dictionary definitions, plus dozens more slang and metaphorical uses, so I sympathize with you here.

Here, to roll someone is to rob or to scam them, as Cascabel has noted. But furthermore, this usage has become conflated with a type of Internet prank known as rolling, with a separate origin, but one that also carries a sense of trickery.

In Collins, see verb meaning 24 of roll:

(transitive) informal, mainly US and New Zealand
to rob (a helpless person, such as someone drunk or asleep)

The archetypical roll in American English is to roll a drunk; imagine a drunkard passed out on the floor, and turning the body over to steal his wallet or jewelry. One who preys on drunks is thus a drunk-roller or jack-roller, the latter term originating with thieves and prostitutes who targeted lumberjacks, who got paid in a lump sum at the end of the season, and would be flush with cash and whiskey.

Metaphorically, if someone gets rolled in a negotiation, they have been swindled or cheated; they are so incompetent or hapless that they might as well have been asleep.

In Internet culture, duckrolling began on the 4chan discussion forum around 2006. It began as a joke where egg was replaced with duck on the board, resulting in the word eggroll being replaced with duckroll, prompting someone to post an image of a duck with wheels, prompting someone else to create a video clip of this duck with its wheels spinning, prompting still others to advertise one video but link to this one instead.

This gave rise to the much better-known prank of rickrolling. Instead of the rolling duck, the surprise clip in a rickroll is the music video of Rick Astley's 1987 song Never Gonna Give You Up

As such, rolling in Internet slang refers to trickery where one thing is advertised but something else entirely is provided, not unlike a bait-and-switch scam in commerce. If someone is rolled, he or she has fallen prey to the trick.

In the column, Hohmann points out that Congressional Democrats were able to force the administration to make many concessions, even though both houses as well as the White House are controlled by the Republicans. He attributes this to the inexperience of the Trump administration, whose lack of understanding of the rules seems to have allowed them to be rolled, whichever way you interpret it.