A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

run high • run low
run high —
1
. (of the sea) have a strong current with a high
tide: The sea runs high, and the boat may be dashed to pieces
on the rocks. 2. (of disputes, feelings, etc.) be strongly mani-
fested or intensify: Popular passions ran high as the general
election approached.
run low —become scarce in supply: We had to return to
camp because our food supply was running low.
run into a stone wall • run one’s head into a stone
wall
run into a stone wall —(also: come up against a brick wall)
encounter an impenetrable obstacle or difficulty: These rec-
ommendations have run into a stone wall, as Republican and
Democratic governors alike have strongly resisted any Federal
cuts.
Note:__The_expression_does_not_correlate_in_meaning_with_the__phrase_hit_the_wall_running'>Note: 
The expression does not correlate in meaning with the
phrase hit the wall running—(coll.) exhaust one’s supply of
energ y during a run (such as a marathon): I could quit running
at any time and just get off the treadmill at any point without
a need to walk (or crawl) home after I hit the wall running.
run one’s head into a stone wall —(coll.) persist with smth.
without making any progress (also: run one’s head into a brick
wall): If the President continued to insist on his plan he would
be beaten. They besought Jimmy Roosevelt to make the Pres-
ident see reason, to persuade him not to run his head into a
stone wall.
Note:
The expression is not equivalent in meaning to the phrase
be stonewalled—
1
. used of a person whose progress is doggedly
blocked (by refusing an answer, cooperation, etc.): They suffered
an unusual tragedy, but I could never find out the full facts
about it — I was stonewalled. No one would tell me the truth.
2. used of parliamentary obstruction of a debate, bill, etc. by
engaging in delaying tactics: This is the same legislation which
was passed unanimously by the Senate during the last session,
but which was stonewalled in the House.