Senate Republicans introduced a tax bill Thursday that would raise federal taxes on millions of Californians by eliminating the individual deduction for state and local taxes, a move that puts the state’s GOP House members in a ticklish situation.

The legislation poses a stark choice for those 14 Republicans, many from suburban districts of the kind where Republicans got crushed in Tuesday’s election. If they support a bill party leaders say is vital to remaining in power by proving that the GOP-dominated Congress can pass significant legislation, they will have to explain to their constituents why they voted to raise their taxes. Or they can vote against a tax bill that is the top priority of the party and President Trump.

Only one California Republican, Darrell Issa of Vista, who narrowly won re-election in his suburban San Diego County district last year, has come out against the House version of the bill, in part because of its treatment of state and local taxes.

And in a telephone interview Thursday, Issa said the Senate bill goes “from bad to hopeless.” One reason is because while the House bill ends deductions for state and local income and sales taxes, it allows for up to $10,000 in property tax deductions. The Senate bill eliminates the entire deduction.

“The House bill needed to deal fairly with the recognition that Californians should not pay taxes on the same income twice,” Issa said.

But his main objection to the Senate bill is that it delays for a year the corporate tax cuts intended to spur growth. Issa described that as “fraudulent on its face.”

He said businesses will simply delay investment decisions by a year, even though Senate tax writers continue to claim economic benefits. “You don’t get a return on an investment you never made,” Issa said. “It’s frustrating that the Senate doesn’t seem to have two businessmen to rub together.”

Issa, a wealthy former businessman, blasted what he called the “marketing material” distributed by House leaders claiming that all taxpayers will see their taxes go down, saying, “It’s just not true.”

Issa said it’s impossible to claim that “everyone gets a tax cut, and that adds up to about $3 trillion, and then turn around and say, we’re doing it with $1.5 trillion.”

The nonpartisan Tax Policy Center estimates that by the end of a decade, more than a quarter of individual taxpayers would see a tax increase, about 38 million people.

Part of the reason is the state and local deduction, which has been a trouble spot for Republicans since they began their effort this fall to slash corporate tax rates from 35 to 20 percent. Even allowing for a $1.5 trillion increase in the deficit that the tax bills would produce within 10 years, lowering business taxes requires reducing or eliminating many deductions that benefit middle- and upper-middle-income taxpayers.

One of the largest is the state and local deduction, which especially helps taxpayers in Democratic-leaning states that tend to have higher taxes.

More than a third of Californians use the deduction, on average deducting $18,437 from their income, according to calculations by the Government Finance Officers Association.

Under pressure from New York Republicans, House tax writers watered down their elimination of the deduction by exempting up to $10,000 in property taxes.

But while that helps New Yorkers, it does little for Californians, whose property taxes tend to be comparatively low thanks to a decades-old ballot measure, Proposition 13, but who pay the nation’s highest state income tax. California Republicans — Rep. Kevin McCarthy of Bakersfield is the second-ranking Republican in the House and responsible for rounding up the votes — have been publicly quiet about the provision.

Now the Senate bill would eliminate the deduction entirely. Gov. Jerry Brown last month called the tax legislation “an attack on California and New York and New Jersey and other states that did not vote for Trump.”

House and Senate Democrats have pounced on both bills, arguing that their tax benefits are heavily weighted toward very high-income taxpayers, which independent analyses confirm. The bills eliminate or slash several taxes paid by the wealthy, such as the alternative minimum tax and the estate tax.

White House officials argue that because wealthy people pay the bulk of income taxes, it is impossible to cut taxes without benefiting them disproportionately, a reversal from earlier claims by White House economic director Gary Cohn that the tax plan would not benefit the wealthy.

The House Ways and Means Committee approved the House tax bill on a party-line vote Thursday, with Republican Devin Nunes of Tulare voting yes. McCarthy announced that the House would vote on the plan next week, not specifying a day.

Rep. Mike Thompson, a St. Helena Democrat on the committee, said the House bill retains a provision that he said would eliminate deductions for personal losses due to fires, earthquakes and other natural disasters, but keep it for losses from recent hurricanes.

McCarthy said in a statement that the bill “lives up to its name — cutting taxes for individuals, families and businesses of all size, and delivering more jobs and higher wages for the American people.”

Republicans are hoping to pass combined House and Senate tax legislation by year’s end and send it to Trump to sign.

Sen. Lindsey Graham, R-S.C., said that if Republicans fail to do so, “The party fractures, most incumbents in 2018 will get a severe primary challenge, a lot of them will probably lose, the base will fracture, the financial contributions will stop, other than that it’ll be fine.”

House Minority Leader Nancy Pelosi of San Francisco said Republicans “have it all wrong,” if they think their tax legislation will keep them in power, citing Tuesday’s election results. Noting the Senate bill’s elimination of the state and local deduction, she said House leaders are forcing vulnerable suburban Republicans to “walk the plank” for a bill that will harm their own constituents.

Those members “should be worried, very, very worried,” Pelosi said. She has scheduled a news conference in San Francisco on Friday with Oakland Democrat Barbara Lee to highlight the state and local deduction in what she calls the “GOP tax scam.”

Asked whether California Republicans are laying low because one of their own is in the leadership, Issa said, “Certainly Kevin’s (McCarthy) telling people this is a good idea carries a lot of weight,” adding, “but Kevin has no real business experience.”

Issa compared the looming vote to the narrow passage of a big Medicare prescription drug benefit during George W. Bush’s administration, when he said GOP leaders assured their rank and file that a yes vote would give them “a permanent Republican majority,” even though they had no plan to pay for the new benefit. Republicans soon after lost their House majority, Issa said.

Carolyn Lochhead is a San Francisco Chronicle staff writer. Email: clochhead@sfchronicle.com Twitter: @carolynlochhead