The administrative delay means that some insurers will continue to set their own out-of-pocket caps next year. The original policy will still take effect in 2015, limiting consumer costs to $6,350 for individuals and $12,700 for families.
Federal officials have defended the move as a show of flexibility toward insurers and employers that need more time to implement the policy.
Lee's statement comes as he and his allies vow to block any necessary spending bills that include money for ObamaCare, a strategy that could force a government shutdown several weeks after Congress returns from August recess.
On Tuesday, Lee urged the House to follow his lead and pass a continuing resolution that "funds the government but not ObamaCare."
GOP leaders are wary of the plan, which establishment Republicans say will inevitably hurt the party if the government shuts down.
But powerful grassroots organizations are working to drum up support for the threat as constituents meet with lawmakers this month.
Lee's statement stood out amid a fairly muted response from Congress to the administrative delay.
Speaker John Boehner (R-Ohio) on Tuesday painted the decision as a "break to big businesses struggling with [Obama's] healthcare law."
But the administration defended its move as a small delay that will not impede the Affordable Care Act's wider benefits for consumers.
"New historic consumer protections under the Affordable Care Act will protect consumers from the worst insurance company abuses, by banning discrimination based on a pre-existing health conditions, ending lifetime and annual limits on what an insurance company will cover, and capping out-of-pocket spending to protect Americans and their families," said an administration official.
“The February guidance builds on these landmark consumer protections by requiring that health plans limit out-of-pocket spending for major medical coverage for the first time, in 2014, on time,” the official added. “This single limit will apply to additional benefits in 2015.”
The decision was outlined on the Labor Department's website in February but went unnoticed until this week.