McConnell and Boehner have a ways to go before they are in the clear, however.
And a familiar endgame — in which Boehner is forced to move legislation through the House with broad Democratic support — could be inevitable.
The House bill is destined for failure in the Senate, where GOP leaders lack the votes to overcome a Democratic filibuster.
Almost the entire Senate Democratic caucus signed a letter Tuesday stating, “the House bill cannot pass the Senate” and urging McConnell to move a clean bill.
A lawsuit is likely to take years to wend its way through the courts, giving little satisfaction to conservative voters who want to see immediate action.
Conservatives have been divided over the McCaul bill, and it is unclear whether GOP leaders can make it more palatable by merging it with Goodlatte’s legislation, which deals with asylum claims and other issues related to enforcement.