With a significantly reduced line-up from the seventeen members on TDA's debut Vongole Fisarmonica, Squeeze This!

captured the group at their transition from a loose ensemble of accordionists into a tighter rock band, featuring a noticeably stronger emphasis on original material under the new leadership of primary singer-songwriter Paul Rogers rather than the cover songs that made up the majority of the preceding album.

In addition to their rock, pop and polka originals, Squeeze This!

covers such broad styles as ska, swing and bluegrass.

The Los Angeles Times praised the album as "fun", putting particular emphasis on the original songs that "inhabit a loopy middle ground between The B-52s and Talking Heads" and making note of the "stylistically credible" musicianship, something which The Santa Cruz Sentinel also echoed, dismissing the "novelty" tag and calling them "inspired performers".