The claim that Democrats like the SAVE America Act is mostly false because multiple reliable sources show that Democrats largely oppose the act, viewing it as a voter suppression measure, although some polls indicate a minority of Democrats support certain provisions.
Democrats like the save America act.

Q&A on the SAVE America Act - FactCheck.org
Source: factcheck.org
Key Evidence
PBS News and NBC News report strong Democratic opposition to the SAVE America Act due to concerns about voter suppression.
A Harvard CAPSHarris poll shows only half of Democrats support it, indicating no broad enthusiasm.
Republican sources acknowledge Democratic opposition publicly.
What the Evidence Shows
The SAVE America Act, a Republican-backed voting legislation, is widely opposed by Democrats who argue it creates barriers to voter registration and disproportionately affects eligible voters, particularly minorities. Sources such as PBS News and NBC News report that Democrats liken the act's requirements, like proof of citizenship and photo ID, to discriminatory Jim Crow-era laws.pbs.orgpbs.orgFact-checking Senate Minority Leader Chuck Schumer on the effects of the SAVE...
nbcnews.comnbcnews.comAmericans support SAVE America Act's photo ID requirement, but Democrats reject...
Facebook posts from Republican Senator Lankford also confirm Democratic opposition. However, a February Harvard CAPSHarris poll cited by FactCheck.org shows that about 50% of Democrats surveyed expressed some support for the act, indicating a divided opinion within the party. National Review, a conservative outlet, argues Democrats should support the act for political reasons, but this is an opinion rather than evidence of actual Democratic support.factcheck.orgfactcheck.orgQ&A on the SAVE America Act
nationalreview.comnationalreview.comDemocrats Should Support the SAVE America Act+1 more
Overall, the dominant stance among Democrats is opposition rather than support.