Republican Party supporters protested Governor Deval Patrick’s proposed increase in the gas tax in front of the State House yesterday morning. (Globe Staff Photo / George Rizer)

Governor Deval Patrick allowed for some flexibility on his gas tax increase proposal yesterday as lawmakers began cautioning that 19 cents could be too high for their constituents.

Patrick told reporters he would be open to a smaller increase, but declined to specify a number, according to the Associated Press. When he unveiled the plan last week, he said he expected legislators to offer alternatives, but did not say how much he would be willing to yield.

He told reporters yesterday that a 4-cent increase would be enough to avert the set of toll hikes approved Tuesday but would not be enough to address all of the state’s transportation problems. He also repeated his vow to veto any bill that does not make the state’s transportation system more efficient.

“As he always does, the governor will work with the Legislature on reaching agreement on a final transportation reform plan,” spokesman Kyle Sullivan said. “However, he has been very clear that he would only support a plan that is comprehensive in nature and includes significant reforms. As he said last week, he will not support any plan that includes both a toll increase and a gas tax increase.”

That stance might put him at odds with some key lawmakers. House Speaker Robert A. DeLeo indicated that 19 cents could be too high to win legislative approval and appeared to suggest that he would support smaller increases in gas tax and tolls.

“As the governor has stated, I think, he’s looking at an either-or,” DeLeo said. “What I’m looking at is a combination.”

A spokesman later said DeLeo opposes the toll increase approved by the Turnpike Authority Tuesday, which would raise tolls in two steps, ultimately doubling the fee at the airport tunnels. Patrick has said the increases would be repealed if the Legislature raises the gas tax.

Senate President Therese Murray’s spokesman, David Falcone, said Murray continues to believe the state will need to raise more money for transportation at some point, but has yet to commit to a means of doing so.

Legislators are receiving tremendous pressure on the issue from interest groups and voters. Representative Joseph F. Wagner, a Chicopee Democrat who cochairs the Legislature’s Joint Transportation Committee, said his office has received as many calls opposing a higher gas tax as it has on any issue during his 18 years in the Legislature.

“I’m guessing that others are going to tell you the same thing,” he said.

Still, Wagner said he was keeping an open mind and pointed out that the tax has not been raised since 1991.

“I think people are likely to offer some acceptance toward an increase in the gas tax if they believe that increase is going to be used prospectively, for improvements in transportation,” he said.

Wagner’s committee has scheduled four hearings to discuss Patrick’s bill and one filed previously by the Senate, which will take place around the state over the next two weeks.

Meanwhile, about two dozen protesters from the state Republican Party spent rush hour in front of the State House, urging drivers to honk to object to Patrick’s transportation bill.

Andrew Ryan of the Globe staff contributed to this report.