Gov. Blagojevich’s pick for the U.S. Senate plans to sit down with Sens. Reid and Durbin at the Capitol.

Sen. Durbin: No plans to seat Burris.

Meanwhile, Burris spoke  Sunday at an evening prayer vigil on Chicago’s South Side, and then addressed his own supporters.

Update: Sens. Reid, McConnell to meet Monday in search of a bipartisan solution.