Regardless of any poster's opinion -- "plowing ahead" with a new bridge just isn't going to happen. First of all, just saying "yeah, we want it to connect 238 with 380" doesn't in any way mean that a straight line between the 101/380 and 238/880 interchange will be anywhere near where planning and vetting will eventually place the facility. Most of the previous plans curved a connector north along the shoreline from north of SFO to Hunters' Point in SE S.F. (the longstanding CA 230 corridor) with an additional connector to I-280 just at the east end of the double-deck segment east of US 101; the bridge itself would extend east at Hunters' Point over to somewhere around Bay Farms (between Alameda and Oakland International Airport), where it would snake down the shoreline a bit to San Leandro, then turn east to access I-238. Originally, a second branch would have sliced through Alameda toward I-980 -- but the political implications of that these days would sink such a connector in its tracks. Any such project will, in the current environmental and political climate, require extensive vetting -- and will probably undergo multiple revisions before both route and format are finalized. One problem with both ends of any projected crossing is that the Bay levels have been rising over the past couple of decades; the mudflats where the CA 230 corridor originally was projected to go are now several feet under water (just drive along the "Candlestick Causeway" section of US 101 to witness this phenomenon first-hand!); some sort of viaduct would be required to complete any connection from the bridge down to the SFO/I-380 area; similar conditions also effect any landing on the east side as well, but there are more options over there for route variances.
The reality is that a project of this magnitude won't be undertaken without having to pass through several layers of the aforementioned "vetting" -- the Bay Conservation district, Caltrans' own bridge engineering department (of course); maybe even the Coastal Commission will put in its two cents' worth, and the various county MPO's (this project would involve three of those)......the list will probably fill out with several more actors as the project progresses through its initial stages. Then there will be the naysayers from S.F. wondering "why the fuck are you considering something that'll bring more cars into the city!" Like any Bay Area project, it'll feature screams of both joy and anguish from collectively all sides! If it progresses beyond the "vague talking about" phase, it'll be an intriguing -- albeit likely bumpy -- ride!