A total of 10 seats would shift among 17 states if the reapportionment of the House were held today, according to an analysis by the Virginia-based consulting firm Election Data Services. That analysis is based on estimates of each state’s population on July 1 that were released early Wednesday by the Census Bureau.

While this overall number of seat switches is within range of previous annual estimates by EDS, there were surprises in the state-by-state projections of seat gains and losses. And perhaps most importantly, the firm’s report underscored how much is still in flux with the actual once-a-decade head count just months away — and how close several states are to the edge of gaining or losing an additional seat.

For example, every previous projection through this decade showed that Illinois would hold on to all 19 House seats it earned in the reapportionment following the 2000 Census. But under the latest projections, Illinois would lose one seat because of slower-than-expected population growth.

In one of the more startling developments, Rhode Island — which throughout the decade appeared set to hold on to both of its House seats — now is projected to slip to just one. That would raise to eight the number of states that only have the single seat guaranteed to each state by the Constitution (the seven single-district states are Alaska, Delaware, Montana, North Dakota, South Dakota, Vermont and Wyoming) — and could also set up a 2012 showdown between Rhode Island’s two Democratic Congressmen, Patrick Kennedy and James Langevin.

Ohio, which had been expected to lose one of its 18 seats ever since the decade’s first 2010 projection, now looks in even worse shape, with a two-seat loss projected.

Heading the other way are South Carolina and Washington, which are now projected to gain one seat each after looking like they would have to settle for what they have. These projected new seats would be South Carolina’s seventh and Washington’s 10th.

But the complicated mathematical formula employed to mete out the 435 House seats is very sensitive to small shifts in population. Kimball Brace, president of Election Data Services, emphasized in his analysis that the gains-and-losses scorecard could vary from the 2009 projections.

On the gainers side, Texas and Arizona — booming states that have made significant seat gains in recent decades — are teetering on adding an additional seat each since the last round of projections. Under the 2009 population estimates, Texas would gain three new seats, for a total of 35. But five of EDS’ six computer models for the actual 2010 Census, based on short-term and long-term population growth trends, showed that Texas will end up with a four-seat gain. Similarly, Arizona is projected to gain one for a total of nine, but three of the six EDS models show the state will end up with a two-seat gain.

At the other end of the spectrum are a pair of states, California and Minnesota, that are now projected to hold all of their seats but have some seat-loss worries based on the computer models.

After decades as the ultimate postwar boom state, California is at risk of losing one of its record total of 53 seats in two of the six EDS models. The 2010 reapportionment already appears certain to be the first in which California will not gain at least one seat since it became a state in 1850, and losing a seat would accent the slowing of its long-running population explosion.

But even more at risk is Minnesota. Although using the 2009 population estimates shows Minnesota barely holding on to its eighth and final House seat, all six EDS models based on population trends show that the state will end up losing a seat after the actual census head count is completed.

One major intangible going into the census is the ultimate population impact of the recession and the accompanying home foreclosure crisis, all of which have hit with particular force in states such as Arizona and Nevada that had been experiencing skyrocketing growth rates.

“We were actually surprised that the new numbers didn’t show even more change in apportionment, given the housing market downturn in the past two years and the onset of the recession this past year,— Brace said.

Despite all the uncertainty in the details, one thing that appears certain is that the post-census seat shifts will continue the pattern, now more than a half-century in the making, of clout in the House migrating from the traditional industrial powerhouse states of the North and Midwest to the sunnier climes of the South and the West. The shift, however, looks considerably smaller than it was in the peak years of the 1970s and 1980s.

All eight states that would gain seats based on the 2009 population estimates are in the South and West: Texas would gain three, with one seat apiece for Arizona, Florida, Georgia, Nevada, South Carolina, Utah and Washington. Of the nine states that would lose seats, only one — projected one-seat loser Louisiana, where the population was devastated by Hurricane Katrina in 2005 — is in the South. The rest are in the Frost Belt: Ohio, with its projected two-seat loss, with one-seat losses for Illinois, Iowa, Massachusetts, Michigan, New Jersey, New York and Pennsylvania.