Reporting by CBS News chief White House correspondent Major Garrett

Top White House officials are discussing whether the GOP-controlled Senate could invite President Trump to deliver the State of the Union address. This, in the wake of House Speaker Nancy Pelosi's suggestion Wednesday that the address be postponed or relegated to being done in writing due to the partial government shutdown, now in its 27th day.

Senate Majority Leader Mitch McConnell's staff hasn't responded yet to CBS News' request for comment.

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Senior administration officials say there is increased talk in the White House about wanting the shutdown ended. But that is paired with a continued insistence that there will be no reopening of the government without the funding Mr. Trump is demanding for a southern border wall -- $5.7 billion.

Senior officials are advising him that Pelosi's suggestion is a sign of weakness -- that Democrats fear he will use the stage to his advantage. It's not known whether that is actually the case, but it is what senior officials are telling him.

The White House is operating on the assumption that Democrats will break and the GOP will remain unified, and the White House has shown no sign of shifting away from its funding-with-reopening demand. Earlier this week, the Trump administration issued a veto threat against measures that would continue to fund the government at current levels. Presenting the bills to Mr. Trump "without a broader agreement to address the border crisis is unacceptable," the statement of administration policy reads.