Support for removing President Donald Trump from office has leapt since House Speaker Nancy Pelosi opened an impeachment inquiry against him, but his Republican backers appear to represent an increasingly loyal minority, according to polls released this week.

As support for impeachment grows, the president’s base is digging in its heels. But he remains disliked and untrusted by most of the country, suggesting that Democrats could find sufficiently broad support for impeachment without converting many Republican voters.

A majority of registered voters now approve of the House’s inquiry into impeaching the president, a poll released Monday by Quinnipiac University showed. A Monmouth University poll of all Americans released Tuesday, meanwhile, found that 49% support the inquiry — just shy of a majority, but still an 8-point jump from August.

Back-to-back Quinnipiac polls in late September — one conducted in the days leading up to Pelosi’s announcement last week, then another taken just afterward — showed that support for Trump’s ultimate removal from office jumped 10 points after the House opened its inquiry. This was driven by a surge among Democrats and a gentler uptick from independent voters.

Voters are now evenly divided on whether Trump should be removed, with 47% saying he should be and the same number saying he should not, according to the latest Quinnipiac survey. Last week 37% of voters said he should be, and 57% said he should not. (The Quinnipiac polls were of only registered voters; most other recent polls have included all American adults.)

Even as Democrats and independents become more supportive of impeachment, there are signs that Pelosi may have a hard time building nationwide consensus.

The share of Republican voters expressing strong approval for Trump’s job performance rose by 12 points since last week, from two-thirds to nearly 4 in 5, according to the Quinnipiac polls. And the share of Republican voters saying Trump is generally an “honest” person has spiked since March, when Quinnipiac last asked the question: from 66% then to 83%.

This suggests that the Republican base’s support for the president might be hardening as he comes under increasingly serious fire — even with evidence mounting that Trump pressured Ukraine’s president, Volodymyr Zelenskiy, to investigate the son of a political rival, former Vice President Joe Biden.

“The number of Republicans who say they approve strongly has risen since last week,” said Mary Snow, a polling analyst at Quinnipiac. “So there is a real partisan divide to these questions.”

The percentage of voters saying they think the president “believes he is above the law” also remains stuck exactly where it was in early May: at 56%, according to the latest Quinnipiac poll. Just 15% of Republican voters hold that view of him.

Independents are split on whether the president should be impeached and removed, but they generally express support for the House’s inquiry. According to a CNN poll of all Americans taken after Pelosi’s announcement, support for impeachment among independents for Trump’s eventual removal is now 11 points higher than it was in May. It stands at 46%, roughly even with the 45% of independents who say he should be allowed to remain in office.

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That number appears poised to move in one direction or the other. When asked in a CBS News poll released Sunday whether it was too soon to say if Trump should be impeached over the Ukraine scandal, roughly a quarter of independents said it was.

In the Monmouth poll, respondents were asked how much they had heard about reports that Trump had asked Zelenskiy to investigate Biden’s son; 27% said they had only heard “a little,” and another 21% said they had heard nothing at all about it.

Whit Dickey, a Republican pollster, said that given the steadiness of Trump’s approval rating throughout his term in office, it seems unlikely to drop significantly during the inquiry. But that approval rating has remained at just over 40%, suggesting that a decisive majority could end up supporting impeachment anyway, Dickey said.