The congressman was asked dozens of times what Congress can do to help federal workers. He said repeatedly that without a congressional majority, Democrats’ hands are tied and urged workers to speak up and share their stories.

“I feel like people should not be in despair and feel like their voice doesn’t matter,” he said. “It matters more than ever, and they need to speak up.”

It may be good politicking for news articles (“next election, go vote Democratic!”), but that’s not really true, not in the US. The Democrats are in a fairly-weak position right now, given that the Republican Party holds a trifecta. But they aren’t out – it’s also possible to get legislators to vote across party lines.

That being said, that requires selling (probably centrist) Republican legislators that crossing lines is actually desirable. It may require making concessions that those particular legislators want.

There are some countries that have strong party discipline. In the UK, for example, it is possible – and happens – for party leadership to mandate that legislators in their party vote in a particular fashion.

https://en.wikipedia.org/wiki/Whip_(politics)#United_Kingdom

Having the whip withdrawn means the MP is effectively expelled from their party. UK parties do not have the power to expel an MP from parliament, but can force the MP to sit as an independent and remove them from ministerial office.

“Losing the whip is seen by many as one of the strongest punishments a political party can dole out to its MPs. The move essentially expels the member from their party, meaning that while they can remain on the green benches, they have to sit as an independent MP.[20]”

“… severe punishment. The most severe is “having the whip withdrawn” - which means you are kicked out of the party within Parliament.”[21]

“Defying a three-line whip is very serious, and has occasionally resulted in the whip being withdrawn from an MP or Lord. This means that the Member is effectively expelled from their party (but keeps their seat) and must sit as an independent until the whip is restored.”[22]

https://www.bbc.com/news/uk-politics-47283976

Boris Johnson has warned Tory MPs threatening to rebel over Brexit they will be barred from standing as Conservatives at the next general election and effectively thrown out of the party.

Up to 20 former ministers, including ex-Chancellors Philip Hammond and Ken Clarke and former Justice Secretary David Gauke, face the prospect of being “deselected” if they support Labour attempts to block a no-deal exit from the EU.

What does being deselected mean?

If an MP is deselected, it means they are removed as a candidate and cannot represent their party at a general election.

The US, in contrast, has relatively-weak party discipline. That is, legislators in a party are comparatively-free to vote as they will; they are more-impacted by what the voters in their particular district want them to do, and less what party leadership wants.

In addition, the current Republican majority in the House of Representatives is a fairly-narrow one, which makes a given legislator voting across party lines much more likely to impact the decisions of that house.

I’d also add, going beyond the party discipline issue at issue here and just having a broader discussion, that in the UK, when a party holds a simple majority in the House of Commons, it has a very great deal of political power, especially since in addition to having stronger party discipline:

• The system is a parliamentary system, which doesn’t really have separation between the executive and legislative branches. This means that normally the executive and legislature are always in pretty close alignment, sort of like holding both the legislature and the executive in the US, as is the case right now.

• The upper legislative house, the House of Lords, is very weak compared to most bicameral systems (and particularly in comparison to the US, where the upper house is strong); nearly all of its political power has been stripped away over the years. This parallels the decline of the power of the aristocracy, which it was intended to represent.

• There are no “supermajority” lines in the UK. In the US, one can hold a majority in a legislative house, but not have a supermajority, and this imposes some limitations on what one might do.

• There is no system of judicial review for laws. In the US, a law might be ruled unconstitutional by the Supreme Court – that is, there is a system of “high law”, the Constitution, which can only be revised by a supermajority of three-quarters of states, and a system of “low law”, ordinary federal laws that cannot conflict with the “high law”. The UK doesn’t do this – there is no higher body of law with a higher bar to revise; Parliament can change anything it wants to via simple majority. So the Supreme Court in the UK – itself a very new institution – can’t say “that legislation Parliament has passed deviates from some constitution and is thus invalid”. It can say that an action that the executive takes is out-of-line with law passed by Parliament and is invalid – it has judicial review over what we in the US would call “regulations” and the UK would call “secondary legislation” – the rules that the executive branch makes. But this really only aims to keep the Prime Minister in line with Parliament’s wishes.