A few thoughts on this interesting topic:
1. Lincoln's speech in which he demanded that Polk identify the exact "spot" on which "Amercian blood had been shed on American soil" was an attempt to get the President to admit that the first skirmish of the war had actually been fought on disputed territory or, worse yet, on Mexican territory.
2. The speech was a failure as Polk ignored it and it resulted in Lincoln being called "Spotty" for some time.
3. The "Spot" speech did not actually adversely affect Lincoln's career in the House. The Whigs of his district had already agreed on the concept of "rotation in office" so Lincloln could not run for re-election and he returnd to Springfield after his one term to resume his legal carreer.
4. Lincloln became the leader of the Whigs in the Illinois legislature and the Spot speech was largely forgotten.
5. When Lincoln returned to national politics as a candidate for the Senate in 1854 the Mexican War was largely an old issue and the fight among the Whigs, the Democrats and the newly forming Republicans was on other issues, most importantly that of expansion of slavery. Lincoln was the leading candidate of the anti slavery coalition in 1854 but could not quite win a majority in the legislature and eventually gave way to an anti-slavery Democrat.
5. When Lincoln ran for the Senate again in 1858, I do not believe that his Spot speech was an issue, although I am sure that at least some supporters of Douglas referred to him at some point in the campaign as Spotty Lincoln just for old times sake.
AH