C172 PLT AND A BE20 HAD AN NMAC IN NCT CLASS E. VARIOUS CTLRS REFUSED TO PROVIDE TA'S BECAUSE OF A TFR IN THE AREA.

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I WAS TRAVELING TO FAT FROM DVO TO PICK UP A FAMILY MEMBER. NORCAL APCH; ZOA; STOCKTON APCH ALL INDICATED THAT THEY WERE TOO BUSY TO PROVIDE TA'S; WHICH I BELIEVE WAS DUE TO THE FACT THAT A TFR OVER FRESNO WAS CAUSING A GREAT DEAL OF WORK FOR CTLRS. AT LEVEL STABLE CRUISE AT 7500 FT; I CAUGHT A GLIMPSE OF MOVEMENT OUT OF MY L PERIPHERY. IT TURNED OUT TO BE SOME SORT OF BUSINESS TURBOPROP; PROBABLY A BEECHCRAFT B200; ON A COLLISION COURSE. I TOOK EVASIVE ACTION (CLB AND BANK) AND AVOIDED A COLLISION. I CAN'T IMAGINE THAT THE OTHER PLT DIDN'T SEE ME; BUT I DID NOT SEE ANY EVASIVE ACTION BEING TAKEN BY THE OTHER ACFT. MY MAGNETIC HEADING WAS 110 DEGS. I BELIEVE THAT THE HEADING OF THE OTHER ACFT WAS ABOUT 250 DEGS. OUR CLOSING VELOCITY WAS QUITE HIGH; PROBABLY MORE THAN 200 KTS. THE MAJORITY OF THE FAULT FOR THE INCIDENT LIES ON MY SHOULDERS AND THE SHOULDERS OF THE OTHER PLT. SEE; BE SEEN; AND AVOID WILL BE TAKEN TO HEART BY ME AND; I HOPE; THE OTHER CREW. THE VALUE OF HAVING ATC PROVIDE SEPARATION WAS UNDERSCORED. IN THE FUTURE; I WILL PROBABLY AVOID HIGH ALT CRUISE UNLESS I CAN GET RADAR ADVISORY SVCS FOR MY VFR FLTS.