Judiciary Chairman Robert W. Goodlatte on Wednesday floated the possibility that the House could eschew a comprehensive approach to overhauling the nation’s immigration system in favor of a step-by-step legislative strategy.

Discussing the matter during an online telecast with Fox News’ Chris Stirewalt, the Virginia Republican appeared committed to most aspects of an immigration overhaul currently being discussed. Goodlatte said legislation must be passed to address the millions of illegal immigrants currently residing in the U.S., fill the need for more high- and low-skilled workers in the high technology and agriculture industries and to upgrade border security.

But Goodlatte, who runs the key committee of jurisdiction in the House for immigration legislation, said Republicans have “definitely left [the] option open” to addressing those and other issues through multiple bills, rather than one comprehensive piece of legislation that includes every component. He praised the bipartisan working groups in the House and Senate that are attempting to reach an agreement on comprehensive legislation.

“Whether we take pieces of this and then put them together later on, or whether we pass something that’s more broad-based remains to be seen, but it’s just going to be what the will of the House will be, this needs to come from the bottom up,” Goodlatte told Stirewalt. “It’s not how fast or slow you go; it’s getting it right.”

Goodlatte, who once worked as an immigration attorney, said hearings on the immigration overhaul have been ongoing, as have weekly briefings with members and staff to educate them on the issues.

There has been some speculation that GOP leaders might bypass committee hearings to avoid Democratic attempts to cause Republicans political problems during any extended debate over immigration. But knowledgeable GOP sources maintain that there is virtually no way that strategy would be adopted on an issue as sensitive and potentially explosive as immigration, particularly in light of Speaker John A. Boehner’s guarantee to switch gears from the last Congress and move major legislation through “regular order.”

It’s unclear if all three committees of jurisdiction will get a crack at the eventual immigration legislation or set of bills, but Goodlatte’s Judiciary Committee was described by one GOP sources as a “lock” to exercise oversight of the overhaul.

Goodlatte praised Sen. Marco Rubio, R-Fla., for his demand that the Senate engage in a methodical approach to considering a comprehensive immigration rewrite. Rubio, a member of the bipartisan “gang of eight” that is currently crafting a bill, has urged the majority Democrats to allow the Senate whatever time is required to fully vet and amend the legislation his group produces. Goodlatte suggested that he favors a similar process in the House.

“Marco Rubio is well to say let’s make sure we are completely and carefully examining this. They should do that over in the Senate and hold additional hearings after they have a product. We are definitely going to be doing that in the House,” Goodlatte said. “It’s my hope that we’ll be producing legislation in the House very soon.”