It’s unclear what impact, if any, the rules would have on Pfizer’s $150 billion proposed tie-up with Allegran PLC. But leading Members of Congress from both parties for now appear to agree on a pair of points: First, that only legislative action can conclusively stem the tide of these so-called corporate inversions; and second, that lawmakers won’t be rallying behind any such solution soon.

The problem, in short, is that most Congressional Republicans — who control both sides of the Capitol — don’t favor a narrow fix aimed at clipping the wings of companies looking to relocate. They view that approach as all-stick, no-carrot, when what’s needed instead is a comprehensive revamp of the corporate tax code that lowers rates sufficiently that companies won’t want to leave. And Republicans don’t expect to make progress on that sort of wholesale tax reform until the next administration.

“The only way you’re going to get that problem solved is to bring down corporate tax rates and make them competitive with the rest of the world,” Sen. Orrin Hatch (R-Utah), chairman of the tax-writing Senate Finance Committee, told Fortune. “We know how to do it, we just need a different president in order to do it.”

Some prominent Democrats agree that lawmakers should only address inversions in the context of a tax-code rewrite. Hatch’s Democratic counterpoint on the Finance panel, Sen. Ron Wyden (D-Ore.), called inversions “a virus” that’s “growing and it is mutating. And the reality is you are not going to be able to fix this with a Band-Aid. It’s going to take fundamental reform.”

There was some bipartisan interest over the summer in tackling a piece of the tax puzzle — bringing home the stash of corporate profits already sitting overseas — as a means to fund domestic infrastructure investments. Those talks included then-House Ways and Means Chairman Paul Ryan (R-Wisc.), who’s since ascended to Speaker, but never amounted to an agreement.

Now, a measure to extend a raft of corporate tax breaks that expire at the end of the year offers a long-shot opportunity for a provision targeting inversions to hitch a ride into law. Though Wyden expressed a preference for dealing with the issue in a broader reform package, he also floated it as a potential bargaining chip in the pending negotiations with Republicans over how many of the expiring corporate breaks are extended permanently. “We’ll have an opportunity… to get into that,” he said. “Obviously we’re looking for everything we can to respond to this, because it is draining the tax base of our country.”

The possibility remains remote.

Rep. Kevin Brady (R-Texas), newly installed atop the House Ways and Means Committee, in a statement said the new Treasury rules would only make American companies “more attractive takeover targets for foreign corporations” by locking them in “an even more uncompetitive tax system.” Instead, he said, policymakers should redouble their efforts to rewrite the code. But one of his colleagues — Rep. Scott Garrett (R-N.J.), a senior member of the House Budget Committee — underlined that that reform is hardly imminent. “We’re wrapping up this year,” he said. “It’s not going to happen now.”