Serious question, why is being fired from your government job a due process issue while being fired from your private sector job is not? If tomorrow, all government jobs were made At Will and the pay increased accordingly, what property of due process has been violated?
If I fire you from your government job because you said something I didn't agree with, being that I'm an acting agent of the government, am I violating your First Amendment? This would not apply to a private employee firing someone for the same reason because they are not an acting government agent.
No, it's not, unless there's some particular legislation at issue, which is generally rare and targeted at specific industries.
Anything the government does is a Due Process issue. Due Process is a very complicated subject, but fundamentally the issue is this: the Federal government is composed of three separate, co-equal branches: legislative, executive, and judicial. At a very basic level and with rare exception (i.e. national security), Due Process means that the government (here, the executive branch) must be accountable; that is, anything the executive branch does which might deprive someone of a right must be reviewable for legality by the courts in case a person wants to challenge the action. If the executive didn't have some affirmative burden to justify, a priori, its actions, then except for the most gross violations the courts would be relegated to rubber stamping executive decisions. In other words, when the legal justifications for executive action are hidden from the courts, the executive is effectively usurping the power of the courts to decide on the constitutionality of government actions.
Reviewable means that there has to be a paper trail documenting the reasons for an action, such that a court can reasonably conclude that an action was a lawful exercise of power. Even when the executive has wide latitude, it typically must still document why it made a particular decision. If an action is not properly reviewable, often times the courts will restore the status quo ante as the courts will not assume that the action was legal merely on the say-so of the executive. How this plays out depends on context.
When courts say that someone has a "property interest" in their Federal employment, they're alluding to a set of relatively high legal standards that must be met before the government can take away certain pre-existing benefits. (They're not alluding to the Takings Clause.) You also have a "property interest" in granted Social Security benefits. Some Due Process contexts have less strict standards for reviewability (i.e. for a detention or arrest often all the courts expect--or could ever expect--is an officer's stated justification), and some contexts have higher standards (administrative agencies like the FCC, particularly ones with significant discretion, often have to document in exacting and excruciating detail their reasons for instituting or changing a rule.)
But Due Process is a fundamental (if not the fundamental) principle in Anglo-American law--that the government must be able to account for its action such that they can be reviewed for legality by courts. This is an affirmative burden, and was the very first limit on power imposed on the sovereign. (See, e.g., the Magna Carta.) Because it's so fundamental you cannot simply remove this burden altogether. Historically and conceptually it's the one restraint from which all the other restraints on government power flow. It's most important to safeguard whenever a lone individual is subject to government discretion; and especially in such cases it's really difficult to craft exceptions that don't swallow the rule or which migrate to other contexts. Normally when the government tries to game the courts by relying on legal technicalities, the courts can, theoretically at least, see through the ruse and change how the law should be applied by resorting to the underlying substantive facts. But when you weaken Due Process you weaken the court's ability to see and consider the substantive facts, thus you weaken their power to restrain the government categorically.
This is entirely unlike the private sector. In the private sector there is no such underlying affirmative burden wrt reviewability. Corporations can and do destroy paper trails, such as by requiring employees to discard documents older than a year or two. Unless they're knowingly (more or less) destroying evidence of a crime, and not violating some specific legislation regarding record keeping (e.g. the relatively recent Sarbanes-Oxley), it's perfectly legal even though the reasons for doing this are exactly to make it prospectively more difficult to hold them accountable in any future court case. Due Process, like Free Speech, is about restraining the government. It has nothing to do with private behavior, per se. So, for example, when you speak of Due Process in the context of a private civil suit, the issue is preventing the court (i.e. the government) from acting capriciously or favoring one litigant over another, and Due Process rules apply to litigants only in so far as they're necessary to properly restrain and channel the power of the court. But generally speaking, unless and until a court or other government actor becomes involved, principles of Due Process are irrelevant to the private actors.
