Washington (CNN) A new CNN poll conducted by SSRS finds a growing share of Americans want to see the GOP abandon its effort to repeal and replace the 2010 health care law known as Obamacare, as majorities across party lines want congressional Republicans to aim for a bill with bipartisan support.

Overall, 35% in the poll say they'd like President Donald Trump and the Republicans in Congress to give up their plans for repealing and replacing Obamacare, up from 23% who said the same in a March survey.

A majority still favor some form of repeal (34% would prefer repeal with replacement at the same time, and 18% favor repeal regardless of whether the law is replaced at the same time). The share in favor of repeal without replacement has held roughly steady since March; it remains the least popular option.

But public preferences are shifting away from repealing the law and enacting replacements concurrently (down from 59% in March), and more now say they're unsure how they want Republican leaders to proceed (13% say so in the new poll).

Increases in support for abandoning repeal have come largely among groups that aren't central to the GOP's base: Younger adults, non-whites and those with lower incomes have become notably more supportive of leaving the ACA as is.

On the growing uncertainty, the percentage of respondents in a poll who say they don't know how they feel about an issue is often related more to the methodology and administration of the survey than to real uncertainty about an issue, however, given the real-life uncertainty about the Senate's plan to replace the ACA while the poll was in the field, in this case, it's possible there's been a meaningful increase in unknown feelings about the law itself.

The poll also finds that with several failed efforts at repealing and replacing the bill in the rear view mirror, about half think it's likely the President and Republicans in Congress will ultimately be able to reach a deal to repeal and replace Obamacare. That's down from 58% who felt it was likely in an April CNN/ORC survey, but remains above the share who say it's unlikely the ACA will be repealed and replaced (41%).

Republicans themselves remain optimistic that their party's leaders in the White House and Congress will be able to come together to achieve this long-standing goal, 78% say it's very or somewhat likely to happen, but less than half of independents or Democrats agree.

Overall, almost eight in 10 in the new poll say they'd like Republicans in Congress to try to work with Democrats to pass a health care bill that has bipartisan support (77% say so). Just 12% favor continuing to try to pass a bill that only has GOP backing. Even among Republicans, only about a quarter favor an approach that only has the backing of Republican lawmakers.

Interviewing for the CNN poll conducted by SSRS was completed July 14-18 among a random national sample of 1,019 adults. The survey included 405 respondents reached on landline telephones and 614 reached on cellphones. The margin of sampling error for the full sample is plus or minus 3.7 percentage points.