Ryan, who was asked about it in a Heritage Foundation Forum in Washington, described the issue as "the thing we have to get over."
"The general interest is going to have to trump over the special interest," the Wisconsin Republican said.
The deduction is a popular tax break that affects nearly one-third of filers and lets them deduct levies like state income taxes and property taxes. It's been in place since the federal income tax was created in 1913 and has survived previous efforts to eliminate it.
Republican leaders have been hearing out the concerns of Republicans from states like New York, New Jersey, California and Illinois in recent weeks. It's unclear whether the plan will continue to entirely nix the deduction or whether a compromise will be struck.
Like other critics of the deduction, Ryan argued that it helps prop up "big government states" and encourages them to keep levying high taxes, since taxpayers will ultimately be able to write them off. It creates a situation in which "states that actually got their act together pay for states that didn't," he said.
Ryan said members need to "see the big picture" and argued that middle class taxpayers will benefit "no matter what state you come from," because of other changes to the tax system, like a doubling of the standard deduction and the lowering of individual tax rates, as proposed in the plan.
But with little details released so far from the plan, Republican members complain that it's difficult to show their constituents the big picture.
Ryan also ramped up pressure on Senate Democrats to join Republican ranks in passing the bill, saying he "can't imagine" that Democrats from manufacturing states like Indiana, Missouri, or North Dakota (all states represented by vulnerable Democrats and states in which President Donald Trump has spoken about taxes) won't vote for the bill.
"I can't imagine we're not going to get some of these votes from some of these Democrats," he said.