No, they do not.  As noted in this post, Timothy McVeigh as executed less than four years after sentence.  He voluntarily gave up one of the many steps, appeal from the denial of collateral relief, but the case went through all the other steps.

Congress has made clear that review of capital cases should be handled expeditiously.  In 18 U.S.C. §3595(a), Congress provided that an appeal from a death sentence "shall have priority over all other cases."

From the date of affirmance of the direct appeal through the Supreme Court, the inmate has one year to file a collateral review motion under 28 U.S.C. §2255.  Again, Congress has provided, "The ... adjudication of any motion under section 2255 by a person under sentence of death, shall be given priority by the district court and by the court of appeals over all noncapital matters."

The federal government has an advantage over states in that there is normally only one round of collateral review, not two.

We need the Department of Justice, if it is going to live up to its name, to insist on prompt completion of these cases and to start frequently taking up writs if these statutes are ignored.