"Could we get jammed? Yes," he said. "Does this member have confidence that we're going to get concessions, meaningful concessions, from the Senate? Likely not."
Perry also suggested that a conference committee likely won't be holding a ton of formal meetings to hash out their agreement.
"When you say 'conference,' people have in their mind something where everybody sits around the table and talks about different things, works out (differences)," he said. "That could be what it looks like, but I suspect it won't look like that."
House Ways and Means ranking member Richard E. Neal also suggested the conference committee will likely only meet for show. The Massachusetts Democrat said he has "relatively low expectations" and it's likely the Republicans will have most everything done before the committee even has its first meeting. Nonetheless, he said Democrats should still name conferees.
The House is scheduled to vote Monday on a motion to go to conference on the tax bill. Republican leaders added the legislative day to the schedule to get the conference process moving.
House Republicans have more votes to spare than Senate Republicans in terms of passing a final measure or conference report.
Assuming all Democrats remain opposed to the measure, the Senate can lose just two GOP votes -- with Vice President Mike Pence casting a tie-breaking vote -- but the House can lose 22.
Only 13 Republicans voted against the tax bill the House passed Nov. 16. Of those "no" votes, 12 came from members from the high-tax states of New York, New Jersey and California over concerns about the partial elimination of the state and local tax deduction, also known as SALT.
GOP leaders are working on a proposal to partially restore the deduction for state and local income taxes, which is fully repealed in both chambers' bills, to address the concerns of California Republicans. But the Senate would have to agree to that in conference.
That's just one of many issues the two chambers will have to tackle. Other House priorities include eliminating expiration dates for tax cuts for individuals, fully repealing the estate tax and maintaining the corporate rate at no higher than 20 percent.