The common law is similar to UCC § 2-609, but there are significant differences.
Here is the rule: (1) a party has reasonable grounds thinking that the other party will materially breach the contract, then: (2) that party may demand adequate assurance of performance, and (3) if is reasonable to do so, (4) it may suspend its performance until adequate assurance is provided. See Restatement (Second) Contracts § 251.
Note the reference to material breach in (1). UCC § 2-609 requires just that the party think the other party may breach, not that it will materially breach. Note also that (2) does not require a demand in writing.
Note also: There is an exception to the rule if the party seeking to suspend performance has already received the "agreed exchange." The "agreed exchange" is the performance by the other party in exchange for which the party seeking to suspend its performance promised to do that from which it now wishes to be excused.
The following flow chart summarizes the rule.
Hathaway v. Sabin illustrates the rule.