In Season One of House of Cards the Democratic Party is convinced that a Democrat must win the Pennsylvania Governor race, leading to the Russo arc and even making the Vice President step down to return to the Governorship. Why? Why does it matter if the governor is a democrat? Correct me if I'm wrong, but Governors have very little traditional role in Federal Politics, right?
Governors can have a HUGE role in presidential politics.
Elections are run pursuant to state laws and processes and are administered by state election officials. They do have to meet federal standards, but the federal government does not run or administer any elections.
As such, a partisan ally can make a big difference. Look at Republican controlled states, and how many of them have Voter ID laws, which address a problem that does not, statistically speaking, even exist by disenfranchising, potentially, thousands of traditionally demographically Democratic voters. Also, early voting, weekend voting, etc are all up to individual states to determine if they are allowed and to what degree, and those impact different areas and economic strata differently.
In still other states you see the assignment of polling stations and newer vs older polling equipment making an impact on whether voters in an area that supports the "ruling party" gets in and out of the polls, and in other areas they are standing in the cold and rain for hours.
George W Bush's brother was the governor of Florida, the focal point of the contested 2000 presidential contest. Thousands of legitimate voters, mostly from Democratic-leaning demographic groups, were illegitimately purged from the voter rolls (Florida admitted in court it was wrong, promised to fix it, and has done it again in each presidential election since). Gore "lost" the state by a tiny fraction of one percent. The full recount was stopped by SCOTUS, so the original actions of the voting officials, partisan politicians aligned with George W Bush's brother, Jeb, wound up standing, as is. Had they been Democratically partisan, it probably would have swung the other way.
In Wisconsin, due to horrible political corruption, there was a NON-partisan election administration agency. The state GOP, after multiple investigations into illegal campaigning, just dissolved it, which means all bets are off for the next election, because there's no one there to enforce any election rules or laws.
All of that are indications of state-level impacts on federal elections.
Also, if, say, I were US president, and I offered a cabinet position or an ambassadorship in a tropical island paradise to a current US Senator from the other party, or she or he had to resign over a scandal... then the governor would choose the replacement (assumed to be of the governor's own party) to serve the rest of the term. A majority in the Senate could be flipped if one party's Senator had to be replaced by the other's governor.