WASHINGTON (AP) -- Senate Republicans are considering a trigger that would automatically increase taxes if their sweeping legislation fails to generate as much revenue as they expect. It's an effort to mollify deficit hawks who worry that tax cuts for businesses and individuals will add to the nation's already mounting debt.

The effort comes as a second Republican senator, Steve Daines of Montana, announced Monday that he opposes the tax bill in its current form. Previously, Sen. Ron Johnson, R-Wis., said he opposed the bill, leaving Senate Republicans no room for error as they hope to vote on the bill this week.

Both senators complained that the tax bill favors large corporations over small businesses. Republicans have only two votes to spare in the Senate, where they hold a 52-48 edge and anticipate Vice President Mike Pence breaking a tie.

At the White House, President Donald Trump maintained that the bill would help all Americans.

"I think it's going to benefit everybody," the president said. "It's going to mostly benefit people looking for jobs more than anything else, because we're giving great incentives."

Senate Republicans indicated that they still had a way to go to secure the votes.

"We're making progress, minute by minute, hour by hour, day by day. But we're not there yet," said Texas Sen. John Cornyn, the No. 2 Republican in the Senate. Pressed on timing, he said the expectation is a vote this week.

A new congressional estimate says the Senate tax bill would add $1.4 trillion to the budget deficit over the next decade. But GOP leaders dispute the estimate, saying tax cuts will spur economic growth, reducing the hit on the deficit.

Many economists disagree with such optimistic projections. The trigger would be a way for senators to test their economic assumptions, with real consequences if they are wrong.

"Do we have realistic numbers and is there a backstop in the process just in case we don't?" asked Sen. James Lankford, R-Okla.

"We should build in the 'What if?' What if this doesn't work?" Lankford said. "What changes might be needed in the tax code in the days ahead to be able to adjust in what scenario?"

Sen. Bob Corker, R-Tenn., said the Trump administration and Senate Republican leaders are open to some kind of a trigger to increase revenues if the tax plan falls short.

Neither Corker nor Lankford spelled out exactly how the trigger would work, noting that senators are still working on the proposal. Sen. Rob Portman, R-Ohio, said the trigger is possible. But, he added, the proposal could run afoul of the Senate's byzantine budget rules.

Trump and Senate Republicans scrambled Monday to make changes to the bill in an effort to win over holdout GOP senators and pass a tax package by the end of the year. Corker said he spoke to White House Chief of Staff John Kelly and economic adviser Gary Cohn throughout the weekend, and Treasury Secretary Steve Mnuchin was at his Senate office on Monday.

"Very possible," Corker said when asked if he might vote "no" in the Senate Budget Committee on Tuesday if the revenue issue isn't settled. "It's important for me to know we've got this resolved," he said.

Johnson told Wisconsin reporters on Monday, "If we develop a fix prior to committee, I'll probably support it, but if we don't I'll vote against it."

Trump and Senate leaders are trying to balance competing demands. While some senators fear the package's debt consequences, others want more generous tax breaks for businesses. In a boost for the legislation, Republican Sen. Rand Paul of Kentucky said he would back the measure.

Trump hosted Republican members of the Senate Finance Committee at the White House on Monday. GOP leaders were still trying to round up the votes in the Senate to pass the bill.

Whatever the Senate passes must be reconciled with the House version of the tax bill.

Trump suggested he is open to making unspecified changes to the way millions of "pass-through" businesses are taxed, a sticking point for some lawmakers. These are businesses in which profits are passed onto the owners, who report the income on their individual tax returns. The vast majority of U.S. businesses, big and small, are taxed this way.

Both Daines and Johnson said the current bill doesn't cut business taxes enough for these types of partnerships and corporations. Johnson gets substantial income from such companies, including a manufacturer he helped found in Wisconsin and a commercial real estate company, according to his financial disclosure statements.

Johnson said Trump has assured lawmakers there will be changes. Trump is to travel to Capitol Hill on Tuesday to lobby Republican senators personally.

The overall tax package blends a sharp reduction in top corporate and business tax rates with more modest relief for individuals.

In signaling his support, Paul wrote in an op-ed on Fox News: "I'm not getting everything I want -- far from it. But I've been immersed in this process. I've fought for and received major changes for the better -- and I plan to vote for this bill as it stands right now."