Republicans who control two-thirds of the nation's governorships are gathering this week in America's largest red state, in part to strategize about how to maintain their political dominance.

But electoral defeats last week, unfulfilled congressional promises, and President Trump's plummeting popularity have some attendees concerned about a shifting political landscape.

Vice President Mike Pence will be the keynote speaker during the two-day gathering of the Republican Governors Association, which kicks off Wednesday in Austin, Texas.

Some of the former Indiana governor's ex-colleagues may need a pep talk. Just as some Democrats facing tight midterm elections once shied away from former President Barack Obama, there might now be Republicans tempted to tip-toe away from their party's leadership.

"The national environment is affecting every elected official at every level," said Republican political strategist Matt Mackowiak.

He said the Trump administration and GOP-controlled Congress still can deliver wins on policies such as tax cuts. But if that doesn't happen, Mr. Mackowiak said, "There are going to be questions about not getting the benefits of Washington being fully run by Republicans."

Earlier this year, Democrats lost special congressional elections in Kansas, Montana, Georgia, and South Carolina, but last week won the governorships in Virginia and New Jersey. The party also erased a previously dominant Republican majority in the Virginia House and gained control of Washington state's Senate.

Republicans will still hold a 33 to 16 advantage in governorships nationwide after January. Alaska Gov. Bill Walker is an independent up for re-election next year.

The Democratic successes revealed some potentially troublesome trends for Republicans. In Virginia, suburban women failed to turn out strongly for GOP candidates. In 2016, that demographic helped put Mr. Trump in the White House. By comparison, minority turnout for Democrats was strong.

Republican Governors Association spokesman Jon Thompson called the results a "voice of displeasure with some things that are happening in Washington."

Republicans in Congress failed to make good on their promise to "repeal and replace" Obama's health care law and are still trying to craft a tax cut plan with sufficient support to pass. Meanwhile, Trump's approval ratings are sagging and the investigation into Russia's meddling in last year's election has accelerated.

Even so, Mr. Thompson said Republicans should not panic.

"You already have Republican governors in some blue states that have their own brand separate from Washington," said Thompson, pointing to Charlie Baker of Massachusetts and Larry Hogan of Maryland.

Having a sizeable advantage in governors' offices means the GOP will have to play more defense in 2018. Thirty-six states are electing governors – Republicans will try to hold 26 compared to the Democrats' nine. That includes 12 open governorships currently held by Republicans, and four open seats now held by Democrats.

The gubernatorial races are important for a reason other than political bragging rights: In many states, governors will play a key role in the next round of redistricting after the 2020 Census.

Republicans have full control of 31 state legislatures, the bodies that typically draw congressional and legislative maps. A Democratic governor in a state where Republicans control the legislature, for example, can limit the type of extreme gerrymandering that would entrench Republicans in political power.

Democratic Governors Association spokesman Jared Leopold said pro-GOP legislative maps drawn by Republicans after the last census have made winning back statehouses this cycle "especially challenging." But he said that, if his party can win a lot of next year's governor's races, Democrats can at least wield veto power over districts drawn to favor the GOP.

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"The governors' races in 2018 will shape congressional maps for a decade to come," Mr. Leopold said.

This story was reported by The Associated Press.