"Conservative," "liberal," and "progressive" don't mean what you think they mean. But it's not your fault.
In common American parlance, we use "conservative" to refer to those who want a smaller government — meaning lower taxes, less spending (especially domestic welfare spending), and a less active regulatory state. Of course, the term has implications for social and foreign policy, too, but the connection there isn't quite as strong. Consider that we use modifiers like "social conservatism" or "paleo-conservatism" or "neo-conservatism" to specify some of those positions, but no modifier is necessary to communicate the affection for small government.
"Liberal" and "progressive," meanwhile, are used almost interchangeably to designate those who want a bigger government — meaning higher taxes (mainly on the rich, of course), more spending (again, principally on social programs), and a more active regulatory state.
These definitions are deeply misleading. They are holdovers from an earlier era of American politics that have become anachronistic, sowing confusion and frustration in the process.
Properly understood, all three of these approaches are fundamentally positional, which is to say each only exists in reference to the politics and culture of the present and recent past. None of them offers a static vision of the proper role of government and shape of society like what we get from non-positional views like socialism, libertarianism, or monarchism.
Properly understood, a progressive is someone who looks at their country and government as it is now and recently has been and offers ideas for how to advance, or progress, the human condition, significantly (though not entirely) through positive government action. A liberal is someone who, on making the same assessment, has suggestions for liberalizing, which is to increase individual choice, equality, and freedom. A conservative is someone who takes in the same view and attempts to conserve valued aspects of the status quo, whether by maintaining them or, if they have recently declined, reviving those traditions.
As you can see, the starting point for any of these views is of enormous importance. What is progressive in one context may be conservative in another. A program that is liberalizing in a very restrictive time and place might itself be restrictive in a more liberal society.
The contrast with content-based philosophies like socialism, libertarianism, or monarchism is evident: A socialist, for example, wants to move toward collective ownership of the means of production and distribution regardless of starting point. The path to that goal might vary depending on whether it begins with feudalism or anarchy or liberal democracy or what have you, but the socialist's ideal is not positional.
In American politics, we've come to define positional terms incorrectly because we've tied them to their referential location from about a century ago. To be conservative in the time of Calvin Coolidge meant conserving small government, because that was the position of the United States in the present and recent past of the 1920s. It is not the present and recent past of the United States today, saddled as she is, for better or worse, with a sprawling state bureaucracy whose scale and scope has long since grown past anything that might be reasonably called "small."
Thus, to be conservative today cannot mean to be an advocate of small government. That is a goal that can be sought — and is sought by libertarians or those with some libertarian impulses — but it is not a status quo that can be conserved.
And that brings me to the Republican government of President Trump, House Speaker Paul Ryan, and Senate Majority Leader Mitch McConnell. The GOP brands itself as America's conservative party, and that's true, but not in the way the GOP itself and the bulk of the American public believes. Republicans are conservative (as indeed are many Democrats, notably in the Hillary Clinton wing of the party), but only under the correct definition, which is to say they like to keep things mostly as they are. They seek to conserve what they value in the status quo and recent past.
You can see this truth writ large in the GOP's failure to repeal and replace ObamaCare despite promising to do exactly that and controlling both houses of Congress plus the White House. To get rid of ObamaCare, at this point, would mean making an enormous change to the status quo, which is not conservative in the proper sense of the word.
This equally explains why, for all the talk about reining in Washington, electing a Republican government does not produce any substantial cuts to the size and scope of the state. Republican administrations don't make government radically smaller because doing so is not conservative from the current starting point.
Republican conservatism also at once explains the GOP's lust for the great, big, beautiful border wall as well as its failure, so far, to actually build it. (I must pause here to note the too-ignored fact that border walls and fences already cover just about all the parts of our southern border where they realistically can be built.) The wall is intended to maintain the United States' cultural and political status quo, but actually building it, particularly with Mexico footing the bill, would be a new and therefore in this sense non-conservative thing.
This disparity between how the GOP's conservatism is broadly understood and how it functions in governance is at once fostered and concealed by our sloppy political language. I confess that I don't have much hope of that sloppiness going away; attempts to reclaim or redefine words in popular conception are almost never as effective as their advocates intend. Still, without some change to our public lexicon, or at least an update to the reference point of these positional terms, that confusing, frustrating disparity will only grow.