One reason is that both parties are "Big Tent" and the nearest two contenders for third party in the modern election system (Libertarian Party and Green Party, as the 3rd largest and 4th largest respectively) generally can find enough common ground with a political faction within in one of the two parties (Most moderate Republicans are Libertarian, which in the States is synonymous with being classical liberal minarchists as opposed to the more anarchist Libertarians in Europe, and the Green Party tends to find common ground with far-left Democratic parties.).
It's not that coalitions exist, but it takes place in intra-party politics rather than inter-party politics like in Germany. Additionally, American Political parties are not as tightly restrictive on their members votes in Congress as many European politics. If the Democratic party is opposed to a bill before congress, they will generally have a published opinion... but that doesn't stop an elected democrat from voting against their party for a number of reasons (mostly job security... if you're in a district that is prone to being a swing district, you're more prone to crossing the asile as that middle/centrist/moderate wing isn't something to sneak at. Typically the middle ground is very unpredictable and easy to flip and if you won on narrow margins, you tend to not be a permanent fixture on Capital Hill to begin with.
Despite Gerrymandering being a thing in the U.S., all but seven states are subdivided into single member districts (those 7 only have one representative, so they aren't divided) and the lower house, which is historically the more politically unstable of the two houses (by design, by the way), and members of either party are more on the hook for their political agendas when they are opposed to local political agendas. If the local economy is a fishing industry, if their representative backs an environmental bill that costs the fishing industry as a result, that representative might not get reelected. And Representatives get re-elected every two years. The Upper House tends to be more stable as terms are for 6 years with one third being re-elected every two years. While the Red/Blue/Swing state phenomena is widely known, if you look at any U.S. map of national elections breaking down by either county or congressional district, you'll see most "solid color states" aren't that solid in color at the lower levels. California, Texas, and Florida are the three largest states by population AND are each the largest Blue (Democrat), Red (Republican), and Swing states (respectively) in the nation. Looking at these state, at a district level, you'll see plenty of districts held by the un-favored party. And while this tends to follow Urban-Rural divide, Florida gets a check as the state is very much Republican except for the more densely packed and strongly favors Democrats to the point that the state is competitive (it's so close that on more than one occasion, Florida has gone to recount to ensure that they counted the number properly). It's not helped that even in reliably democrat controlled Miami, the Cuban Vote is generally pro-Republican (the Republican Party tends to take a stronger stance against Castro-Cuba than the Democrats... and when you're fleeing because of Castro, that's a vote getter).
So since both parties will often have many members that have to be more moderate than the party's typical base. In fact, it's often the party in the majority that has a more difficult time getting what they want done than the minority party, since it's a lot easier to agree on a negative than it is on a positive. The minority party doesn't have to be unified as to what part of a bill is preventing them for saying new, but all parts have to agree for the majority. And typically, the members of the majority are more likely to cross the aisle than the minority because of this fact.
As a final note, as I'm not sure about German's use of political terminology, but in the United States, the leader of the majority in the lower house is not "the government" as it would be called in the UK English. Americans typically use "administration" to mean the same thing the British refer to as "government". Government to an American English speaker typically means all three branches (Legislative, Executive, and Judicial) and not "the policies of the current idiot in charge". In the U.S. the President of the United States and his "administration" typically forms policy with in the confines of laws passed Congress. This is different from Germany where the President of Germany is usually a more cerimonial post while the Chancellor, the leader of the largest party in the majority coalition has much more political power and makes the policy to the execution of laws. The U.S. Speaker of the House is leadership with in the House and may be writing laws for a President who is not of the Speaker's party. This is, in the U.S., typically called divided government and generally denotes a situation where the two houses of congress (the senate and house of representatives) and the Presidency are not all held by one political party. In fact, for the current decade (2010-2020) there have only been three years where all three political bodies have been controlled by the same party in majority (2011 ended Democrat control of the House, 2016-2018 saw Republicans gain the White House, having reclaimed the Senate two years previously. Keep in mind that votes are held in November while the change of office typically occurs in January, with the House and Senate beginning shortly after New Years Day and the Presidency being on January 20th.)