The major housing policy and bond bill expected to pass the House this week includes ideas that have the support of a majority of Massachusetts residents across demographic and political groups, like allowing people to build accessory dwellings on their property and tax incentives to encourage housing production of various types, according to a new poll.

But top House Democrats chose not to allow municipalities to impose new taxes on high-dollar real estate transactions, despite similarly strong support for the idea in the latest University of Massachusetts Amherst/WCVB poll.

Housing was the most mentioned issue when respondents were asked to name the most important issue facing the state, according to the results released Monday morning. Given the chance to pick one issue they would like Gov. Maura Healey and the Legislature to tackle in the next year, 34% of those polled pointed to the state’s “housing shortage and affordability” problem. And residents seem open to any number of ways to address the problem — all six policy proposals polled won the support of a majority of respondents.

Home sales across Massachusetts sank to a 12-year low last year, and housing here is inaccessible or unaffordable for many residents. Healey identified housing last year as “the No. 1 issue facing this state” and said there is a shortage of 200,000 units across the state that must be filled to keep up with population growth and stem the loss of talented workers.

The House Ways and Means Committee redrafted Healey’s five-year, $4.12 billion housing bond bill (H 4138) into a $6.2 billion package teed up for debate Wednesday.

Tatishe Nteta, provost professor of political science at UMass Amherst and director of the poll, said “it is no surprise” that housing is seen by residents as both the most important problem facing the state and the one that residents most want Healey and the Legislature to tackle, given that 44% of people who tried to buy a home here in the last year said they could not find a suitable one in their price range and 63% of those looking for a rental said they could not find an affordable place to live.

“With unified government now a reality in the Bay State and overwhelming support across demographic and political groups for the governor and Legislature to deal with this crisis, voters likely expect movement on this issue as soon as possible. While failure to address the housing conundrum may not have electoral consequences in the 2024 election, if the problem persists, expect the housing crisis to be used as the rationale to ‘throw the bums out’ in 2026 and beyond,” Nteta said.

The housing policy idea that got the greater support (73% strongly or somewhat support) was providing tax breaks to developers to convert empty office buildings into housing, something Healey included in bill and is also in the House version. The second-most supported policy was allowing local governments to limit how much rents can be increased each year (72% strongly or somewhat support), a measure that was not included in Healey’s bill or the House bill.

Residents also support allowing accessory dwelling units by right in single-family zoning districts across the state (66% strongly or somewhat), along with tax breaks for developers who will build more low-income housing (66% strongly or somewhat).

The poll showed support for allowing cities and towns to tax real estate transactions valued at more than $1 million to raise money for local affordable housing (62% strongly or somewhat), a measure supported by Healey but not included in the House bill.

Though it still was supported by a majority of respondents (55% strongly or somewhat), the MBTA Communities Act that requires towns close to MBTA service to zone for multifamily housing near transit services was the least-supported housing policy polled by UMass and WCVB. That law has been met with some resistance at the local level, but state officials maintain it is essential to chipping away at the Bay State’s housing deficit.

“Given the severity of the housing crisis in the state, it should be no surprise that strong majorities of Massachusetts residents support a wide range of innovative policies to increase the supply of affordable housing, including allowing homeowners to add small accessory dwelling units to their houses, and allowing local governments to tax real estate transactions above $1 million to help raise funds for local affordable housing. These are policies proposed by Gov. Healey that the state Legislature could consider as they seek to address the housing crisis,” poll co-director and UMass Amherst and professor of political science Jesse Rhodes said.

Nteta added that the poll did find “muted support among conservatives, Trump voters and Republicans for solutions to the housing crisis that will increase taxes with majorities of each these groups opposing increased taxation for real estate transactions over $1 million.”

Asked who or what is most responsible for Massachusetts’ housing problem, 29% of respondents placed the blame on high interest rates. The Massachusetts Legislature snagged the second-largest share of the blame pie (16%), followed by local governments and housing builders (each with 14%), and landlords (13%), the poll said.

Rhodes noted that one challenge ahead for Massachusetts is that “it takes a lot of planning and coordination between state government, local governments, and builders to increase the supply. And that takes time.”

And though housing was the issue of greatest significance to voters in the latest UMass/WCVB poll, Rhodes said that the widespread concern “is a microcosm of a bigger challenge facing the state — the high cost of living.”

“Massachusetts residents are very frustrated with how expensive the necessities of life are here. This concern may help explain why more than one-third (37%) of Massachusetts residents — and almost 40% of those 18-29 — have considered leaving the state during the last year,” he said. “This dynamic is not good for the state, as Massachusetts needs to retain young people in order to ensure a vibrant future for the commonwealth.”

YouGov interviewed 741 respondents and then pared down the sample to 700 people to be “politically representative” of Massachusetts’ gender, age, race, and education demographics. The poll was in the field from May 17 to May 30 and its results have a margin of error of 4.4%.